supplementary angles math problem solving

Supplementary Angles

What are supplementary angles.

Answer: Supplementary angles are angles whose sum is 180 °

No matter how large or small angles 1 and 2 on the left become, the two angles remain supplementary which means that they add up to 180°.

Do supplementary angles need to be next to each other (ie adjacent)?

Answer: No!

Supplementary angles do not need to be adjacent angles (angles next to one another).

Both pairs of angles pictured below are supplementary.

Angles that are supplementary and adjacent are known as a linear pair .

Interactive Supplementary Angles

Click and drag around the points below to explore and discover the rule for vertical angles on your own.

You can click and drag points A, B, and C.

(Full Size Interactive Supplementary Angles )

Practice Problems

If $$m \angle 1 =32 $$°, what is the $$m \angle 2 ? $$

$$ m \angle 1 + m \angle 2 = 180° \\ 32° + m \angle 2 = 180° \\ m \angle 2 = 180°-32° \\ m \angle 2 = 148° $$

$$ \angle c $$ and $$ \angle F $$ are supplementary. If $$m \angle C$$ is 25°, what is the $$m \angle F$$?

$$ m \angle c + m \angle F = 180° \\ 25° + m \angle F = 180° \\ m \angle F = 180°-25° = 155° $$

If the ratio of two supplementary angles is $$ 2:1 $$, what is the measure of the larger angle?

First, since this is a ratio problem, we will let the larger angle be 2x and the smaller angle x . We know that $$ 2x + 1x = 180$$ , so now, let's first solve for x:

$$ 3x = 180° \\ x = \frac{180°}{3} = 60° $$

Now, the larger angle is the 2x which is 2(60) = 120 degrees Answer: 120 degrees

If the ratio of two supplementary angles is 8:1, what is the measure of the smaller angle?

First, since this is a ratio problem, we will let the larger angle be 8x and the smaller angle x . We know that 8x + 1x = 180 , so now, let's first solve for x:

$$ 9x = 180° \\ x = \frac{180°}{9} = 20° $$

Now, the smaller angle is the 1x which is 1(20°) = 20° Answer: 20°

Ultimate Math Solver (Free) Free Algebra Solver ... type anything in there!

Popular pages @ mathwarehouse.com.

Angle Pair: Supplementary Angles

Supplementary angles.

If the measures of two angles sum up to [latex]180^\circ[/latex], they are called supplementary angles . You’ll notice that when this pair of angles are adjacent, they form a straight angle. Each angle is called a supplement of the other.

Take for instance the diagram above, [latex]\angle AXN[/latex] and [latex]\angle NXF[/latex] are supplementary. If we add their angle measures ([latex]120^\circ + 60^\circ [/latex]), we get [latex]180^\circ[/latex].

But the angles don’t have to be adjacent nor share a common side and vertex to be considered as supplementary angles.

[latex]\angle H[/latex] and [latex]\angle S[/latex] are supplementary. Why? Because even though they are non-adjacent angles, the sum of their measures is [latex]180^\circ[/latex].

[latex]35^\circ + 145^\circ = 180^\circ [/latex]

Example Problems Involving Supplementary Angles

Let’s delve more into the relationship of this angle pair by going through some examples.

Example 1: Are [latex]\angle ERW[/latex] and [latex]\angle WRQ[/latex] supplementary?

We have to add the angle measures of both angles in order to find out if they sum up to [latex]180^\circ[/latex].

And they do! Therefore, [latex]\angle ERW[/latex] and [latex]\angle WRQ[/latex] are supplementary angles .

Example 2: If [latex]\angle CYM[/latex] and [latex]\angle LKG[/latex] are supplementary, what is the measure of [latex]\angle CYM[/latex]?

We are only given the measure of [latex]\angle LKG[/latex]. However, since we know that supplementary angles add up to [latex]180^\circ[/latex], we can simply use subtraction in order to find the measure of [latex]\angle CYM[/latex].

Thus, the measure of [latex]\angle CYM[/latex] is [latex]\textbf{127}^\circ[/latex].

Example 3: [latex]\angle JBU[/latex] and [latex]\angle UBT[/latex] are supplementary. Find the missing angle measure.

This problem is similar to our previous example. The only difference is that the two angles are adjacent to each other. However, the concept stays the same. We can find the missing measure by subtracting the given measure of [latex]\angle UBT[/latex] from [latex]180^\circ[/latex].

The missing angle measure or the measure of [latex]\angle JBU[/latex] is [latex]\textbf{42}^\circ[/latex].

This makes sense because if we add both angle measures, we get [latex]180^\circ[/latex].

[latex]138^\circ + 42^\circ = 180^\circ [/latex]

This proves that both angles are indeed supplementary.

Example 4: What is the value of [latex]x[/latex]?

Just by looking at the diagram, we can tell that [latex]\angle PVH[/latex] and [latex]\angle HVA[/latex] are supplementary. Together, the angle pair form a straight angle while adjacent to each other. A straight angle measures [latex]180^\circ[/latex] and so are supplementary angles.

Both of the angle measures are given but one is expressed in the form of an algebraic expression. It may look challenging but it’s really not. Since we know that they are supplementary, we will set up our equation such that the sum of the angle measures is [latex]180^\circ[/latex]. Then we solve for [latex]x[/latex].

So, the value of [latex]x[/latex] is [latex]\textbf{9}[/latex].

To check if we got the correct answer, let’s plug in the value of [latex]x[/latex] into our original equation. If both sides of the equation equal to [latex]180[/latex], then we got the correct value for [latex]x[/latex].

Perfect! [latex]9[/latex] indeed is the correct value for [latex]x[/latex]. While checking, we also found out that the measure of [latex]\angle HVA[/latex] is [latex]61^\circ[/latex].

Example 5: Suppose [latex]\angle Q[/latex] and [latex]\angle F[/latex] are supplementary. Find the measures of the two angles.

Here we are given two supplementary angles whose measures are expressed in algebraic expressions. Let’s go ahead and set up our equation then solve for the variable [latex]x[/latex].

Now that we know the value of [latex]x[/latex], we can use this to find the measure of each angle. We’ll simply replace [latex]x[/latex] with [latex]7[/latex] on each of the algebraic expressions then simplify.

So the measure of [latex]\angle Q[/latex] is [latex]\textbf{156}^\circ[/latex] and the measure of [latex]\angle F[/latex] is [latex]\textbf{24}^\circ[/latex].

If we add both angle measures, we get [latex]180^\circ[/latex] which means our answers are correct.

[latex]156^\circ + 24^\circ = 180^\circ [/latex]

Example 6: Two supplementary angles are such that the measure of one angle is 3 times the measure of the other. Determine the measure of each angle.

Let [latex]x^\circ[/latex] be the measure of the first angle. Since the second angle measures 3 times than the first, then it will be [latex]3x ^\circ[/latex]. Keep in mind that the angles are supplementary so the right side of the equation must be [latex]180 ^\circ[/latex].

Using the value of [latex]x[/latex], the measure of the second angle will be [latex]3x = 3\left( {45} \right) = 135[/latex].

Therefore, the measures of the angles are [latex]\textbf{45} ^\circ[/latex] and [latex]\textbf{135} ^\circ[/latex] which when added sum up to [latex]180 ^\circ[/latex] .

You might also like these tutorials:

• Alternate Exterior Angles
• Alternate Interior Angles
• Complementary Angles
• Corresponding Angles
• Vertical Angles

Supplementary Angles

When the sum of the measures of two angles is 180°, such angles are called supplementary angles and each of them is called a supplement of the other.

Angles of 60° and 120° are supplementary angles. 

The supplement of an angle of 110° is the angle of 70° and the supplement of an angle of 70° is the angle of 110°

Observations:  (i) Two acute angles cannot be supplement of each other.  (ii) Two right angles are always supplementary.  (iii) Two obtuse angles cannot be supplement of each other. 

Worked-out Problems on Supplementary Angles: 1. Verify if 115°, 65° are a pair of supplementary angles. Solution: 115° + 65° = 180°

Hence, they are a pair of supplementary angles.

2. Find the supplement of the angle (20 + y)°. Solution: Supplement of the angle (20 + y)° = 180° - (20 + y)°

= 180° - 20° - y°

= (160 - y) °

3. If angles of measures (x — 2)° and (2x + 5)° are a pair of supplementary angles. Find the measures. Solution: Since (x - 2)° and (2x + 5)° represent a pair of supplementary angles, then their sum must be equal to 180°.

Therefore, (x - 2) + (2x + 5) = 180

x - 2 + 2x + 5 = 180

x + 2x - 2 + 5 = 180

3x + 3 = 180

3x + 3 – 3 = 180 — 3

3x = 180 — 3

x = 59° Therefore, we know the value of x = 59°, put the value in place of x

= 57° And again, 2x + 5

= 2 × 59 + 5

Therefore, the two supplementary angles are 57° and 123°. 

4.  Two supplementary angles are in the ratio 7 : 8. Find the measure of the angles.  Solution:  Let the common ratio be x. 

If one angle is 7x, then the other angle is 8x. 

Therefore, 7x + 8x = 180 

15x = 180 

x = 12 Put the value of x = 12

One angle is 7x 

= 7 × 12 

= 84°  And the other angle is 8x  = 8 × 12

= 96° 

Therefore, the two supplementary angles are 84° and 96°. 

5.  In the given figure find the measure of the unknown angle. 

Solution: x + 55° + 40° = 180°

The sum of angles at a point on a line on one side of it is 180°

Therefore, x + 95° = 180°

x + 95° - 95° = 180° - 95°

●  Lines and Angles

Fundamental Geometrical Concepts

Classification of Angles

Related Angles

Some Geometric Terms and Results

Complementary Angles

Complementary and Supplementary Angles

Adjacent Angles

Linear Pair of Angles

Vertically Opposite Angles

Parallel Lines

Transversal Line

Parallel and Transversal Lines

7th Grade Math Problems

8th Grade Math Practice   From Supplementary Angles to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math . Use this Google Search to find what you need.

New! Comments

Share this page: What’s this?

• Preschool Activities
• Kindergarten Math
• 1st Grade Math
• 2nd Grade Math
• 3rd Grade Math
• 4th Grade Math
• 5th Grade Math
• 6th Grade Math
• 7th Grade Math
• 8th Grade Math
• 9th Grade Math
• 10th Grade Math
• 11 & 12 Grade Math
• Concepts of Sets
• Probability
• Boolean Algebra
• Math Coloring Pages
• Multiplication Table
• Cool Maths Games
• Math Flash Cards
• Online Math Quiz
• Math Puzzles
• Binary System
• Math Dictionary
• Conversion Chart
• Homework Sheets
• Math Problem Ans
• Free Math Answers
• Printable Math Sheet
• Funny Math Answers
• Employment Test
• Math Patterns
• Link Partners
• Privacy Policy

Recent Articles

Subtracting 2-digit numbers | how to subtract two digit numbers.

Sep 29, 24 11:08 PM

Properties of Subtraction |Whole Numbers |Subtraction of Whole Numbers

Sep 26, 24 02:54 PM

Subtraction of Numbers using Number Line |Subtracting with Number Line

Sep 26, 24 12:42 PM

2nd Grade Subtraction Worksheet | Subtraction of 2-Digit Numbers | Ans

Sep 25, 24 04:37 PM

3rd Grade Addition Worksheet | 3-Digit Addition | Word Problems | Ans

Sep 25, 24 01:32 PM

© and ™ math-only-math.com. All Rights Reserved. 2010 - 2024.

Supplementary Angles

These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°:

Notice that together they make a straight angle .

But the angles don't have to be together.

These two are supplementary because 60° + 120° = 180°

Play With It ...

(Drag the points)

When the two angles add to 180°, we say they "Supplement" each other. Supplement comes from Latin supplere , to complete or "supply" what is needed

Spelling: be careful, it is not "Suppl i mentary Angle"

Complementary vs Supplementary

A related idea is Complementary Angles , they add up to 90°

How to remember which is which? Well, alphabetically they are:

• Complementary add to 90°
• Supplementary add to 180°

You can also think:

• " S " of S upplementary is for " S traight" (180° is a straight line)

Or you can think:

• when you are right you get a compliment (sounds like compl e ment)
• "supplement" (like a vitamin supplement) is something extra, so is bigger

MathBootCamps

Supplementary angles and examples.

Supplementary angles are angles whose measures sum to 180°. In the lesson below, we will review this idea along with taking a look at some example problems. [adsenseWide]

Example problems with supplementary angles

Let’s look at a few examples of how you would work with the concept of supplementary angles.

The two angles lie along a straight line, so they are supplementary. Therefore: \(x + 118 = 180\). Solving this equation: \(\begin{align}x + 118 &= 180\\ x &= \boxed{62} \end{align} \)

The angles \(A\) and \(B\) are supplementary. If \(m\angle A = (2x)^{\circ}\) and \(m\angle B = (2x-2)^{\circ}\), what is the value of \(x\)?

Since the angles are supplementary, their measures add to 180°. In other words: \(2x + (2x – 2) = 180\). Solving this equation gives the value of \(x\).

\(\begin{align}2x + (2x – 2) &= 180\\ 4x – 2 &= 180\\ 4x &= 182\\ x &= \boxed{45.5} \end{align} \)

The previous example could have asked for some different information. Let’s look at a similar example that asks a slightly different question.

The angles \(A\) and \(B\) are supplementary. If \(m\angle A = (2x+5)^{\circ}\) and \(m\angle B = (x-20)^{\circ}\), what is \(m \angle A\)?

This time you are being asked for the measure of the angle and not just \(x\). But, the value of \(x\) is needed to find the measure of the angle. So, first set up an equation and find \(x\).

\(\begin{align}2x+5 + x – 20 &= 180\\ 3x-15 &= 180 \\ 3x &= 195\\ x&= 65\end{align}\)

The measure of angle \(A\) is then: \(m\angle A = (2x+5)^{\circ}\) and \(x = 65\)

\(m\angle A = (2(65)+5)^{\circ} = \boxed{135^{\circ}} \)

There isn’t much to working with supplementary angles. You just have to remember that their sum is 180° and that any set of angles lying along a straight line will also be supplementary.

Share this:

• Click to share on Twitter (Opens in new window)
• Click to share on Facebook (Opens in new window)

Supplementary Angles Worksheets

Related Topics: More Math Worksheets More Printable Math Worksheets 6th Grade Math

There are six sets of angle worksheets:

• Angles on a Straight Line
• Angles at a Point
• Vertical Angles
• Complementary Angles

Supplementary Angles

• Complementary & Supplementary Angles

Examples, solutions, videos, and worksheets to help grade 6 learn how to use the supplementary angles property to find unknown angles.

How to use the supplementary angles property?

Supplementary angles are pairs of angles that add up to 180 degrees when combined. In other words, if you have two angles that are supplementary to each other, the sum of their measures is 180 degrees.

Mathematically, if ∠A and ∠B are supplementary angles, you can represent this as:

∠A + ∠B = 180 degrees

Let one of the angles be x degrees. The other angle, which is supplementary to it, will be (90 - x) degrees. For example, if one angle is 60 degrees, the supplementary angle is 180 - 60 = 120 degrees.

Understanding supplementary angles is essential in geometry and trigonometry, as they are used to solve various problems involving angles, such as finding unknown angles in geometric figures or determining the measures of angles in right triangles.

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Supplementary Angles Worksheets .

More Supplementary Angles Worksheets

Printable (Answers on the second page.) Supplementary Angles Worksheet (find unknown angles)

Online Types of Angles Angles in a Straight Line Vertical Angles Complementary Angles Supplementary Angles

Related Lessons & Worksheets

More Printable Worksheets

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

GCSE Tutoring Programme

Our chosen students improved 1.19 of a grade on average - 0.45 more than those who didn't have the tutoring.

In order to access this I need to be confident with:

This topic is relevant for:

Supplementary Angles

Here we will learn about supplementary angles including how to find missing angles by applying knowledge of supplementary angles to a context.

There are also angles worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What are supplementary angles?

Supplementary angles are two angles that add up to 180 degrees. They do not have to be adjacent or share a vertex.

When we add together supplementary angles we get a straight line. This is because a straight line is 180 degrees; the same as the total of supplementary angles.

Before we start looking at specific examples it is important we are familiar with some key words , terminology, rules and symbols required for this topic:

• Angle : defined as the amount of turn around a common vertex.
• Vertex : the point created by two line segments ( plural is vertices) .
• How to label an angle:

We normally label angles in two main ways:

1 By giving the angle a ‘name’ which is normally a lowercase letter/symbol such as a , x or y or the greek letter ϴ (theta).

2 By referring to the angle as the three letters that define the angle. The middle letter refers to the vertex at which the angle is e.g. see the diagram for the angle we call ABC :

• Angles on a straight line equal 180 °:

Angles on one part of a straight line always add up to 180° .

However see the next diagram for an example of where a and b do not equal 180° because they do not meet at one single point on the straight line, i.e. they do not share a vertex and are not adjacent to one another:

• Angles around a point equal 360 °:

Angles around a point will always equal 360° See the diagram for an example where angles a , b and c are equal to 360° :

• Vertically opposite angles:

Vertically opposite angles refer to angles that are opposite one another at a specific vertex and are created by two lines crossing. See below for an example:

Here the two angles labelled ‘a’ are equal to one another because they are ‘vertically opposite’ at the same vertex.

The same applies to angles labelled as ‘b’ .

Note: Sometimes these are called vertical angles

How to solve problems involving supplementary angles

In order to solve problems involving supplementary angles:

• Identify which angles are supplementary. If appropriate write this down using angle notation e.g. AOB + BDE = 180
• Clearly identity which of the unknown angles the question is asking you to find the value of.

Solve the problem and give reasons where applicable.

• Clearly state the answer using angle terminology.

How to solve problems involving supplementary angles.

Complementary and supplementary angles worksheet

Get your free complementary and supplementary angles worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Supplementary Angles examples

Example 1: finding an angle which is supplementary to another.

Two angles, x and y , are supplementary and one of them is 17° . What is the size of the other angle?

Identify which angles are supplementary .

The two angles are supplementary and therefore equal 180° :

2 Clearly identity which of the unknown angles the question is asking you to find the value of .

Find the angle that is not 17° . 

3 Solve the problem and give reasons where applicable .

4 Clearly state the answer using angle terminology .

The size of the other angle is 163° .

Example 2: finding an angle which is supplementary to another

Two angles are supplementary. One is double the size of the other. What is the size of the smaller angle?

The two non-identified angles are supplementary and therefore equal 180° .

Clearly identity which of the unknown angles the question is asking you to find the value of .

You are being asked to find the smaller angle.

Solve the problem and give reasons where applicable .

If you call the first angle a then the other angle must be 2a as ‘one is double the size of the other.’ Therefore a + 2a = 180 . We can now solve this equation

The two angles are therefore of size 60° and 120° .

Clearly state the answer using angle terminology .

The smaller angle is 60° .

Example 3: finding supplementary angles from a diagram

ABC is a right-angled triangle. Which of the following pairs of angles are supplementary?

In this question you are not told which angles are supplementary.

You are trying to find the angles that are supplementary. Therefore we are looking for two angles that when added together equal 180° .

As angles that are supplementary equal 180° you know that two angles that lie on a straight line are therefore supplementary. BDC is a straight line and therefore the two angles either side of D on that lie are supplementary.

Angles BDA and CDA are supplementary. 

Example 4: finding a given angle using supplementary angles

Angles A and B are supplementary to one another.

Find the size of angle B .

The two angles given as A and B are supplementary and therefore equal 180° .

Therefore A + B = 180° .

We can create an equation from the information given:

Remember you need to find the value of angle B so we substitute the value x = 32 into the expression for angle B :

Angle B = 113° .

Example 5: identifying supplementary angles

AB and CD are parallel. Which pair of angles are supplementary,

‘ HGD and GFB’ or ‘HGD and HGC ’ ?

You are trying to find the angles that are supplementary. Therefore you are looking for two angles that when added together equal 180° . Remember you are given a choice of ‘ HGD and GFB ’ or ‘ HGD and HGC ’.

Below is the diagram (given in the question) where the two sets of angles have been labelled separately. This will help you spot which are supplementary.

HGD and GFB .

The angles are both obtuse angles therefore cannot add together to be 180° .

They are also congruent angles and known as corresponding angles because of their relationship within the two parallel lines.

HGD and HGC .

The two angles here lie on a straight line and are therefore equal to 180° and are supplementary.

HGD and HGC are supplementary angles.

Example 6: identifying supplementary angles

Which angles in the below trapezium ABCD are supplementary? You must give your answers using correct angle notation.

A trapezium has one set of parallel lines. From your prior knowledge of properties of a trapezium you know that, when added together, adjacent angles are equal to 180° and are therefore supplementary.

They are also known as co-interior angles because of their relationship with the two parallel lines.

Clearly state the answer using angle terminology. 

There are two sets of supplementary angles

• Angles DAB and ADC
• Angles ABC and BCD

Common misconceptions

These are some of the common misconceptions around the above angle rules

• Incorrectly labelling angles which are supplementary
• Assuming supplementary angles must share a vertex
• Mixing up supplementary angles and complementary angles
• Misuse of the ‘straight line’ rule where angles do not share a vertex
• Finding the incorrect angle due to misunderstanding the terminology  

Related lessons

Supplementary angles is part of our series of lessons to support revision on angle rules. You may find it helpful to start with the main angle rules lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

• Angle rules
• Angles on a straight line
• Complementary angles
• Angles around a point
• Vertically opposite angles

Practice supplementary angles questions

1. Two angles ‘ x and y ‘ are supplementary and one of them is 47^{\circ} . What is the size of the other angle?

The two angles are supplementary, so they must have a sum of 180 and 47+133=180 .

2. Two angles ‘ x and y ‘ are supplementary and one of them is 123^{\circ} . What is the size of the other angle?

The two angles are supplementary, so they must have a sum of 180 and 57+123=180 .

3. Two angles are supplementary. One is three times the size of the other. What is the size of the smaller angle?

The angles make a 180 degree angle. There are three parts in one angle and one part in the other, so four parts in total. If we divide 180 by 4 we get 45 , so this is the size of the smaller angle.

4. Two angles are supplementary. One is 4x – 40 and the other is 5x – 50 . Find the value of x .

The sum of the two angles must equal 180 , so the equation we must solve is 9x-90=180 . Using the standard methods for solving a linear equation gives the solution x=30 .

5. Which angles are supplementary in the diagram below:

Since ABD and DBC meet at a point on a straight line, they must be supplementary as angles on a straight line add up to 180 .

6. How many pairs of supplementary angles does a parallelogram have?

By considering angle rules, we know there are four pairs of co-interior angles in a parallelogram. Since co-interior angles add up to 180 they are supplementary.

Supplementary angles GCSE questions

1. Find the size of the angle marked x .

                                                                                                                                                                                         (1)

(a) Which two pairs of angles are supplementary in this trapezium?

(b) Angle ADC=58^{\circ} . Find the angle BAD .

a) BAD and ADC, ABC and BCD

3. Work out the size of the smaller angle.

Learning checklist

You have now learned how to:

• Use conventional terms and notation for angles
• Define angles that are supplementary
• Apply the properties of supplementary angles
• Apply angle facts and properties to solve problems 

The next lessons are

• Circles, sectors and arcs
• Angles in polygons
• Angles in parallel lines

Still stuck?

Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.

Find out more about our GCSE maths tuition programme.

Privacy Overview

Want Better Math Grades?

✅ Unlimited Solutions

✅ Step-by-Step Answers

✅ Available 24/7

➕ Free Bonuses ($1085 value!)

On this page

• Introduction to Geometry
• Functions and Graphs
• 1. Introduction to Functions
• 2. Functions from Verbal Statements
• 3. Rectangular Coordinates
• 4. The Graph of a Function
• 4a. Domain and Range of a Function
• 4b. Domain and Range interactive applet
• 4c. Comparison calculator BMI - BAI
• 5. Graphing Using a Computer Algebra System
• 5a. Online graphing calculator (1): Plot your own graph (JSXGraph)
• 5b. Online graphing calculator (2): Plot your own graph (SVG)
• 6. Graphs of Functions Defined by Tables of Data
• 7. Continuous and Discontinuous Functions
• 8. Split Functions
• 9. Even and Odd Functions

Related Sections

Math Tutoring

Need help? Chat with a tutor anytime, 24/7.

Online Math Solver

Solve your math problem step by step!

IntMath Forum

Get help with your math queries:

Supplementary Angles: All You Need to Know 

Geometry can be tricky for some students, but understanding supplementary angles is a key concept that can help make other topics in the subject easier to understand. Supplementary angles are two angles whose measurements add up to 180 degrees. Let’s explore this concept further. 

Defining Supplementary Angles 

Supplementary angles are two angles whose measurements add up to 180 degrees. For example, if one angle measures 90 degrees, then the other angle must measure 90 degrees as well in order for them to be considered supplementary. Together, they form a straight line. It’s important to note that while the two supplementary angles do have the same measurement, they are still considered different angles and have different vertexes (the point where two rays meet). 

Using Supplementary Angles 

Knowing how supplementary angles work is important when solving certain geometry problems. For instance, when given only one angle in a problem, you can use your knowledge of supplementary angles to find out what the other missing angle is by subtracting it from 180 degrees. This can be especially useful if you are trying to solve for an unknown triangle or a quadrilateral (a four-sided polygon). In addition, you can use your knowledge of supplementary angles to determine whether or not an object is perpendicular (90 degrees) or oblique (not 90 degrees). By determining which type of object you are dealing with and what kind of angle it has, you will be better equipped to find the measurements of all its sides and corners. 

Conclusion: 

Supplementary angles are an essential concept when it comes to understanding geometry concepts such as triangles and quadrilaterals. Knowing how supplementary angles work can help students more easily solve complex geometry problems by providing them with the necessary information needed to fill in the gaps within their equations. With practice and patience, students will soon become comfortable using supplemental angles within their geometry studies!

What are supplementary angles in geometry?

Supplementary angles are two angles whose measurements add up to 180 degrees. For example, if one angle measures 90 degrees, then the other angle must measure 90 degrees as well for them to be considered supplementary.

Why is it called supplementary angle?

Supplementary angles are so named because they form a straight line when combined, thus supplementing each other. When two supplementary angles are put together, it forms a full rotation of 180 degrees.

What are examples of supplementary angles?

Examples of supplementary angles include an angle that measures 45 degrees and another angle that measures 135 degrees, or an angle measuring 30 degrees and an angle measuring 150 degrees.

Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.

Email Address Sign Up

Child Login

• Kindergarten
• Number charts
• Skip Counting
• Place Value
• Number Lines
• Subtraction
• Multiplication
• Word Problems
• Comparing Numbers
• Ordering Numbers
• Odd and Even
• Prime and Composite
• Roman Numerals
• Ordinal Numbers
• In and Out Boxes
• Number System Conversions
• More Number Sense Worksheets
• Size Comparison
• Measuring Length
• Metric Unit Conversion
• Customary Unit Conversion
• Temperature
• More Measurement Worksheets
• Writing Checks
• Profit and Loss
• Simple Interest
• Compound Interest
• Tally Marks
• Mean, Median, Mode, Range
• Mean Absolute Deviation
• Stem-and-leaf Plot
• Box-and-whisker Plot
• Permutation and Combination
• Probability
• Venn Diagram
• More Statistics Worksheets
• Shapes - 2D
• Shapes - 3D
• Lines, Rays and Line Segments
• Points, Lines and Planes
• Transformation
• Quadrilateral
• Ordered Pairs
• Midpoint Formula
• Distance Formula
• Parallel, Perpendicular and Intersecting Lines
• Scale Factor
• Surface Area
• Pythagorean Theorem
• More Geometry Worksheets
• Converting between Fractions and Decimals
• Significant Figures
• Convert between Fractions, Decimals, and Percents
• Proportions
• Direct and Inverse Variation
• Order of Operations
• Squaring Numbers
• Square Roots
• Scientific Notations
• Speed, Distance, and Time
• Absolute Value
• More Pre-Algebra Worksheets
• Translating Algebraic Phrases
• Evaluating Algebraic Expressions
• Simplifying Algebraic Expressions
• Algebraic Identities
• Quadratic Equations
• Systems of Equations
• Polynomials
• Inequalities
• Sequence and Series
• Complex Numbers
• More Algebra Worksheets
• Trigonometry
• Math Workbooks
• English Language Arts
• Summer Review Packets
• Social Studies
• Holidays and Events
• Worksheets >
• Geometry >
• Angles >
• Complementary and Supplementary

Complementary and Supplementary Angles Worksheets

Utilize our printable complementary and supplementary angles worksheets to help build your child's skill at identifying complementary and supplementary angles, finding the unknown angles, using algebraic expressions to find angular measures, and more. A highly effective practice tool for grade 6, grade 7, and grade 8, these resources lay a firm foundation for the topic of complementary and supplementary angles. Make use of our free samples and subscribe for instant access to a potpourri of pdf worksheets.

Finding Complementary Angles - Type 1

This complementary angles worksheet requires kids to solve diverse exercises in 3 sections. Students must use the property that the sum of complementary angles is 90° to obtain their answers correctly.

• Download the set

Finding Complementary Angles - Type 2

The name of the game is identifying complementary angles. In this 6th grade exercise, identify the correct complementary pair by inference, match the complementary angles, and answer our in-out boxes.

Finding Unknown Angles in a Complementary Pair

Learn to find the unknown measure of each complementary angle with these worksheets. 7th grade kids keenly observe the right angles and equate them accordingly to find the measure of the unknown angle.

Algebra in Complementary Angles | One-Step & Two-Step

Find the unknown value of complementary angles using only an angle measure and an algebraic expression. Practice evaluating the expression to find the unknown values in one step or two steps.

Finding Supplementary Angles - Type 1

This supplementary angles worksheet drives kids to find the pair whose sum does/doesn't equal 180°, match the angles that form supplementary angles when added, and complete in/out boxes.

Finding Supplementary Angles - Type 2

Get your students to skillfully find supplementary pairs, match the angles, and follow the rules of the given in-out box for correct answers! Reiterate how two supplementary angles make a straight angle.

Finding Unknown Angles in a Supplementary Pair

Make finding the unknown measure of each supplementary angle a super-easy task! Observe the angles in each illustration and equate them accordingly to find the measure of the unknown angles.

Algebra in Supplementary Angles | One-Step & Two-Step

This part of our complementary and supplementary angles worksheets helps 7th grade and 8th grade students to use the fundamental property of supplementary angles and solve for x in either one or two steps.

Identifying Complementary and Supplementary Angles - Type 1

Inspire 6th grade and 7th grade children to find the complementary and supplementary angles for a given set of problems. Also, match the complement and supplement of the angles with this pdf set.

Identifying Complementary and Supplementary Angles - Type 2

Let your competence in identifying complementary and supplementary angles progress steadily. Identify the correct pairs by inference, find the measure of the angles, and answer the in-out boxes with precision.

Finding Unknown Angles in a Complementary or Supplementary Pair

Train students to keenly observe the right angles and straight angles and equate them to find the measure of the unknown angle in these printable complementary and supplementary angles worksheets.

Complementary and Supplementary Pairs | Adjacent and Non-Adjacent Angles (Multiple Rays)

Ready to demonstrate greater skills in finding the complementary and supplementary angles? Every pdf here contains 8 image-specific questions that test your understanding of multiple rays.

Algebra in Complementary and Supplementary Angles | One-Step & Two-Step

A right or straight angle with an angle measure and an algebraic expression is given. 7th grade and 8th grade students must set up the equation, perform inverse operations and solve for x in 1 or 2 steps.

Related Worksheets

» Pairs of Angles

» Angles Formed by a Transversal

» Linear Pairs of Angles

» Angles Around a Point

Become a Member

Membership Information

Printing Help

How to Use Online Worksheets

How to Use Printable Worksheets

Privacy Policy

Terms of Use

Copyright © 2024 - Math Worksheets 4 Kids

This is a members-only feature!

COMPLEMENTARY AND SUPPLEMENTARY ANGLES PROBLEMS AND SOLUTIONS

Problem 1 :

Find the measure of an angle that is twice as large as its supplement.

Let x be the measure of the required angle.

The measure of a supplement of the angle  x is (180 ° - x).

Given : T he measure of an angle that is twice as large as its supplement.

x = 2(180 ° - x)

x = 360 ° - 2x

Add 2 x to both sides.

Divide both sides by 3.

Therefore, the required angle is 120°.

Problem 2 :

Find the measure of an angle that is half as large as its complement.

The measure of a complement of the angle  x is (90 ° - x).

Given : T he measure of an angle that is half as large as its complement.

Multiply both sides by 2.

2x = 90 ° - x

Add x to both sides.

Therefore, the required angle is 30°.

Problem 3 :

The measure of a supplement of an angle is 12 more than twice the measure of the angle. Find the measures of the angle and its supplement.

Given : The measure of a supplement of an angle is 12 more than twice the measure of the angle.

180 ° - x = 2x + 12 °

180 °  = 3x + 12 °

Subtract 12 from both sides.

168°  = 3x

180 ° - x = 180 ° - 56 ° = 124°

Therefore, the measure of the angle is 56° and its supplement is 124°.

Problem 4 :

A supplement of an angle is six times as large as a complement of the angle. Find the measures of the angle, its supplement and its compliment.

The measure of a complement and a supplement of the angle  x  are (90 ° - x) and  (180 ° - x) respectively .

Given : A supplement of an angle is six times as large as a complement of the angle.

180 ° -  x = 6(90 ° - x)

180 ° -  x = 540 ° - 6x

Add 6 x to both sides.

180 ° + 5 x = 540 °

Subtract 180° from both sides.

Divide both sides by 5.

Therefore, the measure of the angle is 72°, its supplement is 108° and its complement is 18°.

Problem 5 :

You are told that the measure of an acute angle is equal to the difference between the measure of a supplement of the angle and twice the measure of a complement of the angle. What can you deduce about the angle? Explain.

Let x be the measure of an acute angle.

Given :  T he measure of an acute angle is equal to the difference between the measure of a supplement of the angle and twice the measure of a complement of the angle.

x = (180 ° - x) - 2(90 ° - x)

x = 180° - x - 180° + 2x

The above is equation is true for all values of x such that x is an acute angle.

Conclusion :

The measure of any acute angle is equal to t he difference between the measure of a supplement and twice the measure of a complement of the acute angle.

Problem 6 :

Can the measure of a complement of an angle ever equal exactly half the measure of a supplement of the angle? Explain. 

Let x be the measure of the angle.

The measure of a complement and a supplement of the angle  x  are (90 ° - x ) and  (180 ° - x ) respectively .

Given : T he measure of a complement of an angle ever equal exactly half the measure of a supplement of the angle.

2(90 ° - x) = 180 ° - x

180 ° - 2x = 180 ° - x

Multiply both sides by -1.

Yes,  the measure of a complement of an angle ever equal exactly half the measure of a supplement of the angle and that angle is  0°.  

Kindly mail your feedback to   [email protected]

We always appreciate your feedback.

© All rights reserved. onlinemath4all.com

• Sat Math Practice
• SAT Math Worksheets
• PEMDAS Rule
• BODMAS rule
• GEMDAS Order of Operations
• Math Calculators
• Transformations of Functions
• Order of rotational symmetry
• Lines of symmetry
• Compound Angles
• Quantitative Aptitude Tricks
• Trigonometric ratio table
• Word Problems
• Times Table Shortcuts
• 10th CBSE solution
• PSAT Math Preparation
• Privacy Policy
• Laws of Exponents

Recent Articles

Complementary and supplementary angles problems and solutions.

Sep 29, 24 09:18 AM

Derivative Problems and Solutions (Part - 10)

Sep 27, 24 02:01 AM

SAT Math Resources (Videos, Concepts, Worksheets and More)

Sep 26, 24 10:14 AM

What are Supplementary Angles?

Knowing about supplementary angles can be very useful in solving for missing angle measurements. This tutorial introduces you to supplementary angles and shows you how to use them to solve for a missing angle measurement. Take a look!

• supplementary
• supplementary angles
• straight angle
• straight angles
• 180 degrees

Background Tutorials

Points and lines.

What is a Point?

A point is a fundamental building block of math. Without points, you couldn't make lines, planes, angles, or polygons. That also means that graphing would be impossible. Needless to say, learning about points is very important! That makes this tutorial a must see!

Planes and Angles

What is an Angle?

Angles are a fundamental building block for creating all sorts of shapes! In this tutorial, learn about how an angle is formed, how to name an angle, and how an angle is measured. Take a look!

What are Acute, Obtuse, Right, and Straight Angles?

Did you know that there are different kinds of angles? Knowing how to identify these angles is an important part of solving many problems involving angles. Check out this tutorial and learn about the different kinds of angles!

Further Exploration

Angle definitions.

What are Complementary Angles?

Do complementary angles always have something nice to say? Maybe. One thing complementary angles always do is add up to 90 degrees. In this tutorial, learn about complementary angles and see how to use this knowledge to solve a problem involving these special types of angles!

Finding Missing Angles

How Do You Use Supplementary Angles to Find a Missing Angle?

If angles combine to form a straight angle, then those angles are called supplementary. In this tutorial, you'll see how to use your knowledge of supplementary angles to set up an equation and solve for a missing angle measurement. Take a look!

• Terms of Use

Supplementary Angles – Definition, Types, Facts, Examples, FAQs

What are supplementary angles, properties of supplementary angles, how to find supplementary angles, solved examples on supplementary angles, practice problems on supplementary angles, frequently asked questions about supplementary angles.

Two angles are said to be supplementary when the sum of angle measures is equal to 18 0 . 

Note that the two angles need not be adjacent to be supplementary. So, what do supplementary angles look like? Take a look!

Recommended Games

Supplementary Angles: Definition

Supplementary angles can be defined as a pair of angles that add up to 180°.

Recommended Worksheets

More Worksheets

• Supplementary angles are a pair of angles that add up to 180°.
• One supplementary angle equals the difference between 180° and the other supplementary angle.
• The adjacent angles formed by two intersecting lines are always supplementary.
• Angles in a linear pair are always supplementary, but two supplementary angles need not form a linear pair.
• Adjacent supplementary angles form a straight line.

What Are Adjacent and Non-adjacent Supplementary Angles?

The supplementary angles can be both non-adjacent or adjacent. What does a supplementary angle look like? Let us move forward to learn about the two types of supplementary angles.

Adjacent Supplementary Angles:

The adjacent supplementary angles are the supplementary angles that share a common vertex and a common side. The angles together form a straight angle (and thus, a straight line). They are also called ‘angles in a linear pair’ or ‘linear pair of angles.’

Example: Consider the following diagram. The angles ∠XOZ and ∠YOZ are adjacent supplementary angles. They share a common vertex O and a common side OZ. 

Also, 60° + 120° = 180°

Non-Adjacent Supplementary Angles:

The non-adjacent supplementary angles are the angles which are not adjacent, but the sum of their measures equals 180 degrees. Any two angles whose sum is 180 degrees are supplementary!

• Measure the angles.
• Add the measurements of the two angles and check if they add up to 180 degrees. 
• The angles will be supplementary if the sum equals 180 degrees.

For two angles X and Y to be supplementary, we must have

m ∠ X + m ∠ Y = 180°

You can also find the other counterpart of a given angle to find two supplementary angles.

Example: What will be the supplementary angle of an angle of 70°?

We know that the sum of two supplementary angles should be 180°

Let us assume the missing angle to be x. 

70° + x = 180°

On solving for x, we get

x = 110°.

Supplementary Angles Theorem and Proof

Statement: If two angles are supplementary to the same angle, they are congruent.

Suppose ∠x and ∠y are two different angles supplementary to a third angle ∠a.

∠x + ∠a = 180° …….(1)

∠y + ∠a = 180° …….(2)

From equations (1) and (2), we get

∠x + ∠a =  ∠y + ∠a

∠x = ∠y

Hence, proved.

Facts about Supplementary Angles

• If two angles are supplementary and one of them is a right angle , then the other angle is also a right angle.
• The supplementary angle of an acute angle is an obtuse angle , and vice-versa.

In this article, we learned about the supplementary angles, definition, properties, and also the theorem.We also discussed how to find supplementary angles. Let us move ahead to the numerical section to have a better comprehension of the concepts through solved examples and practice problems.

Example 1: Two angles are supplementary. Find the other angle if one angle is 80° .

Let the missing angle be x.

x + 80° = 180° …Angles are supplementary.

Solving for x, we get

x = 100°

Therefore, the measure of the other supplementary angle is 100°.

Example 2: Two angles that are supplementary. One angle is 35° greater than the other. Find the missing angle.

Let us assume that the measure of one angle is x°.

Then, other angle = x° + 35°

So, x° + (x° + 35°) = 180°

On simplifying:

2x° + 35° = 180°

2x°= 145°

x° = 72.5°

So, the other angle is:

x° + 35° = 72.5° + 35° = 107.5°

Therefore, 72.5° and 107.5° are the measures of the smaller and larger angles, respectively.

Example 3: What will be the measures of two supplementary angles if the first angle is three times the second angle?

Supplementary Angles - Definition, Types, Facts, Examples, FAQs

Attend this quiz & Test your knowledge.

What is the sum of two supplementary angles?

What will be the other supplementary angle if one angle is 70 degrees, which of the following pairs of angles are supplementary, the supplementary angle of a right angle is always, a pair of supplementary angles are.

Let the smaller angle be x°.

Thus, the larger angle = 3x°.

x° + 3x° = 180° …Angles are supplementary.

On simplifying, we get

4x° = 180°

x° = 45°

So, the larger angle is:

3x° = 3(45°)

x° = 135°

Therefore, 45° and 135° are the values of the two supplementary angles.

Example 4: If two supplementary angles are in the ratio 3 : 2, find the measures of angles.

Solution:  

Let the measures of two angles be 3k° and 2k° respectively.

3k° + 2k° = 180°

5k° = 180°

Now, we get the measures of the two angles.

3k° = (3 × 36)° = 108°

2k° = (2 × 36)° = 72°

Therefore, 108° and 72° are the measures of two supplementary angles.

What is the difference between complementary and supplementary angles?

The complementary angles are a pair of angles that add up to 90°, while the supplementary angles add up to 180°.

Can two acute angles be supplementary angles?

No, two acute angles can never be supplementary because they can never add up to 180°.

Do supplementary angles need to be adjacent?

No, two supplementary angles may or may not be adjacent.

What are angles in a linear pair? Are they supplementary?

Angles in a linear pair are a pair of adjacent angles formed when two lines intersect each other. They are always supplementary.

RELATED POSTS

• Corresponding Sides – Definition, Solved Examples, Facts, FAQs
• Area of a Quarter Circle: Definition, Formula, Examples
• Milliliters to Gallons Conversion
• Distance Between Point and Plane: Definition, Formula, Examples, FAQs
• Common Difference: Definition with Examples

Math & ELA | PreK To Grade 5

Kids see fun., you see real learning outcomes..

Make study-time fun with 14,000+ games & activities, 450+ lesson plans, and more—free forever.

Parents, Try for Free Teachers, Use for Free

• Parallelogram
• Quadrilateral
• Parallelepiped
• Tetrahedron
• Dodecahedron
• Fraction Calculator
• Mixed Fraction Calculator
• Greatest Common Factor Calulator
• Decimal to Fraction Calculator
• Whole Numbers
• Rational Numbers
• Place Value
• Irrational Numbers
• Natural Numbers
• Binary Operation
• Numerator and Denominator
• Order of Operations (PEMDAS)
• Scientific Notation

Table of Contents

Last modified on August 3rd, 2023

#ezw_tco-2 .ez-toc-title{ font-size: 120%; ; ; } #ezw_tco-2 .ez-toc-widget-container ul.ez-toc-list li.active{ background-color: #ededed; } chapter outline

Complementary and supplementary angles.

A pair of angles is sometimes classified based on the result of their addition as complementary and supplementary angles.

What are Complementary Angles

Two angles are called complementary angles if the sum of their measure equals 90°. In other words, if two angles add up to form a right angle they known as complementary angles. Each angle in the pair is said to be the complement of the other.

The word ‘complementary’ came from the Latin word ‘completum’ meaning ‘completed’. To become complementary angles, the two angles do not need to be adjacent. If they are adjacent they will form a right angle.

In the above figure,

∠XOZ + ∠ZOY = 90°, and thus are complementary angels.

How to Find Two Angles are Complementary

If the measure of two angels is given, adding them will prove whether they are complementary.

Mathematically,

Sum of two complementary angles = 90°

Thus, if one of the angle is x, the other angle will be (90° – x)

For example, in a right angle triangle, the two acute angles are complementary. This is because in a triangle the sum of the three angles is 180°. Since one angle is 90°, the sum of the other two angles forms 90°.

Let’s understand the concept using some examples:

As we know, Sum of two complementary angles = 90°, here one angle = 38°, other angle = x Thus, x + 38° = 90° x = 90° – 38° x = 52°

As we know, Sum of two complementary angles = 90°, here first angle = x/2, second angle = x/4 x/2 + x/4 = 90° (2x + x)/4 = 90° 3x/4 = 90° x = 90° x 4/3 x = 120° Hence, ∠ABC = x/2 = 120°/2 = 60° and, ∠XYZ = x/4 = 120°/4 = 30°

If x and y are complementary angles and x = 60°. Find the value of y.

As we know, Sum of two complementary angles = 90° Here, x + y = 90°, here x = 60° 60° + y = 90° y = 90° – 60° y = 30°

The measure of an angle is 22°. What is the measure of its complementary angle?

Let x be the measure of the complementary angel to 22° As we know, Sum of two complementary angles = 90° x + 22° = 90°  x = 90° – 22° x = 68°

Find the complement of the angle 1/2 nd of 100°

1/2 nd of 100° = ½ x 100°  = 50° As we know, Sum of two complementary angles = 90° x + 50° = 90°  x = 90° – 50° x = 40°

The difference between two complementary angles is 48°. Find both the angles.

Let one of the angle be = x° Then the other angle = (90 – x)° Given that difference between the two angles = 48° Now, (90 – x)° – x° = 48° 90° – 2x = 48° – 2x = 48° – 90° – 2x = – 42° x = 42°/2 x = 21° Thus the other angle is,  (90 – x)° = 90° – 21° = 69°

Two angles are complementary. The measure of the larger angle is 10 degree more than thrice the measure of the smaller angle. Find the measure of the smaller and larger angle in degrees.

Let us assume the two complementary angles are x and y, where x is the larger angle and y is the smaller angle. By the given information, x = 3y + 10…… (1) As we know, two angles are complementary, Hence, x + y = 90°…… (2) Putting the value of (1) in (2) we get, x + y = 90° (known) 3y + 10 + y = 90° [∵x = 3y + 10] 4y = 90 – 10 y = 80/4 y = 20° Now, Putting the value of y in (2) we get, x + 20° = 90° x = 90° – 20° = 70° Hence the larger angle (x) = 70° and the smaller angle (y) = 20°

Types of Complementary Angles

As discussed before, two angles need not be adjacent to be complementary to each other; accordingly, they are divided into two types:

1) Adjacent Complementary Angles : Two angles are adjacent complementary angles if they share a common vertex and a common arm. An example of adjacent complementary angles is given below:

In the above figure ∠AOC and ∠BOC are adjacent angles a they have a common vertex O and a common arm OC. Also, they add up to 90°.

∠AOC + ∠BOC = 35° + 55° = 90°

Thus these two angles are adjacent complementary angles.

2) Non-adjacent Complementary Angles : Two angles are non-adjacent complementary angles they are not adjacent to each other.

Here, ∠AOB and ∠XOY are non-adjacent angles as they neither have a common vertex nor a common arm. Also, they add up to 90°.

∠AOB + ∠XOY = 35° + 55° = 90°

Thus these two angles are non-adjacent complementary angles.

Complementary Angles Theorem

Prove Complementary Angles Theorem

The Two Angles that are Complementary to the Same Angle are Congruent to Each Other

Let ∠ZOW is complementary to ∠XOZ and ∠YOW Then, by the definition of complementary angles, ∠ZOW + ∠XOZ = 90°…… (1) ∠ZOW + ∠YOW = 90°…… (2) Adding (1) and (2) we get, ∠ZOW + ∠XOZ = ∠ZOW + ∠YOW Subtracting ∠ZOW from both sides, we get ∠XOZ = ∠YOW Hence Proved

Real Life Examples of Complementary Angles

• When a rectangular piece of bread is divided into two pieces by cutting along the diagonal, we get two right triangles, each with a pair of complementary angles.
• A slice of pizza
• Hands of a clock showing 3PM and the seconds hand pointing towards the digit 2
• A crossroad
• A staircase that have an escalation of 30° and the wall at 90°

What are Supplementary Angles

Two angles are called supplementary angles if the sum of their measure equals 180°. Each angle in the pair is said to be the supplement of the other.

The word ‘supplementary’ came from the Latin word ‘supplere’ meaning ‘supply’. Similar to complementary angles, the two angles do not need to be adjacent. If they are adjacent they will form a straight angle.

∠XOZ + ∠YOZ = 180°, and thus are supplementary angels.

Thus in a pair of supplementary angles:

• If one angel is acute the other is an obtuse angle
• If one angle is 90°, the other angle is also 90°

How to Find Two Angles are Supplementary

If the measure of two angels is given, adding them will prove whether they are supplementary.

Sum of two supplementary angles = 180°

Thus, if one of the angle is x, the other angle will be (180° – x)

As we know, Sum of two supplementary angles = 180°, here one angle = 80°, other angle = x Thus, x + 38° = 180° x = 180° – 80° x = 100°

If x and y are supplementary angles and x = 88°. Find the value of y.

As we know, Sum of two supplementary angles = 180° Here, x + y = 180°, here x = 88° 88° + y = 180° y = 180° – 88° y = 92°

As we know, Sum of two supplementary angles = 180°, here first angle = x/2, second angle = x/3 x/2 + x/3 = 180° (3x + 2x)/6 = 180° 5x/6 = 180° x = 180° x 6/5 x = 216° Hence, ∠AOB = x/2 = 216°/2 = 108° and, ∠XOY = x/3 = 216°/3 = 72°

The measure of an angle is 120°. What is the measure of its supplementary angle?

Let x be the measure of the supplementary angel to 120° As we know, Sum of two supplementary angles = 180°, here x and 120° are supplementary angles x + 120° = 180°  x = 180° – 120° x = 60°

Find the supplement of the angle 1/3 rd of 330°

1/3 rd of 330° = 1/3 x 330°  = 110° As we know, Sum of two supplementary angles = 180° Let x be the supplement of 110° x + 110° = 180°  x = 180° – 110° x = 70°

The difference between two supplementary angles is 70°. Find both the angles.

Let one of the angle be = x° Then the other angle = (180 – x)° Given that difference between the two angles = 70° Now, (180 – x)° – x° = 70° 180° – 2x = 70° – 2x = 70° – 180° – 2x = – 110° x = 110°/2 x = 55° Thus the other angle is,  (180 – x)° = 180° – 55° = 125°

Two angles are supplementary. The measure of the larger angle is 6 degree more than twice the measure of the smaller angle. Find the measure of the smaller and larger angle in degrees.

Let us assume the two supplementary angles are x and y, where x is the larger angle and y is the smaller angle. By the given information, x = 2y + 6…… (1) As we know, two angles are supplementary, Hence, x + y = 180°…… (2) Putting the value of (1) in (2) we get, x + y = 180° (known) 2y + 6+ y = 180° [∵x = 2y + 6] 3y = 180 – 6 y = 174/3 y = 58° Now, Putting the value of y in (2) we get, x + 58° = 180° x = 180° – 58° = 122° Hence the larger angle (x) = 122° and the smaller angle (y) = 58°

Types of Supplementary Angles

As discussed before, two angles need not be adjacent to be supplementary to each other; accordingly, they are divided into two types:

1) Adjacent Supplementary Angles : Two angles are adjacent supplementary angles if they share a common vertex and a common arm. An example of adjacent supplementary angles is given below:

In the above figure ∠BCA and ∠DCA are adjacent angles a they have a common vertex C and a common arm OA. Also, they add up to 180°.

∠ BCA + ∠ DCA = 60° + 120° = 180°

Thus these two angles are adjacent supplementary angles.

2) Non- adjacent Supplementary Angles : Two angles are non-adjacent supplementary angles they are not adjacent to each other.

Here, ∠AOB and ∠XOY are non-adjacent angles as they neither have a common vertex nor a common arm. Also, they add up to 180°.

∠AOB + ∠XOY = 35° + 55° = 180°

Thus these two angles are non-adjacent supplementary angles.

Supplementary Angles Theorem

Prove Supplementary Angles Theorem

The two Angles that are Supplementary to the Same Angle are Congruent to Each Other

Let ∠POB is supplementary to ∠AOP and ∠QOB Then, by the definition of supplementary angles, ∠POB + ∠AOP = 180°….. (1) ∠POB + ∠QOB = 180°……(2) Adding (1) and (2) we get, ∠POB + ∠AOP = ∠POB + ∠QOB Subtracting ∠POB from both sides we get, ∠AOP = ∠QOB Hence Proved

Examples in Real Life

• Consecutive angles in a parallelogram
• Cock showing 9’ o clock and 3’o clock
• Slice of pizza
• Lines in a tennis court

Complementary vs Supplementary Angles

Mnemonics and Fun Facts

• The letter ‘c’ for ‘complementary’ and ‘c’ for ‘corner’. Hence when two complementary angles put together to form a ‘corner right’ angle.
• The letter‘s’ for ‘supplementary’ and‘s’ for ‘straight’. Hence when two supplementary angles are put together they form a ‘straight’ angle.
• The letter ‘c’ in complementary comes before the letter ‘s’ in supplementary, just like 90° comes before 180°.

Ans . No, complementary angles are not always congruent. Since complementary angles add up to 90°, the only possible pairs of complementary angles that are congruent are they measure 45°each.

Ans . According to the ‘same side interior angle’ theorem if a transversal intersects two parallel lines, each pair of interior angles on the same side are supplementary

Ans . Yes, all linear pairs of angles are supplementary.

Leave a comment Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

• Privacy Policy
• Trigonometry

Join Our Newsletter

© 2024 Mathmonks.com . All rights reserved. Reproduction in whole or in part without permission is prohibited.

WORD PROBLEMS ON COMPLEMENTARY AND SUPPLEMENTARY ANGLES

Complementary angles :

Two angles are complementary,  if the sum of their measures is equal to 90. 

Supplementary angles :

Two angles are  supplementary angles  if the sum of their measures is equal to 180 degrees.

Problem 1 :

Angles A and B are complementary. If m∠A = 3x - 8 and m∠B = 5x + 10, what is the measure of each angle ?

Since angles A and B are complementary,

m∠A + m∠B = 90

3x - 8 + 5x + 10 = 90

8x + 2 = 90

Subtracting 2 on both sides.

8x = 90 - 2

Dividing by 8 on both sides.

So, the required angles measures are 25 °  and 65 ° .

Problem 2 :

Angles Q and R are supplementary. If  m∠Q = 4x + 9 and  m∠R = 8x + 3, what is the measure of each angle ?

Since angles Q and R are supplementary, they add up to 180 degree.

m∠Q +  m∠R = 180

4x + 9 + 8x + 3 = 180

12x + 12 = 180

Subtracting 12 on both sides.

12x = 180 - 12

Dividing by 12 on both sides, we get

So, the angle measures are 65 and 115.

Problem 3 :

Find the measure of two complementary angles  ∠A and  ∠B, if m ∠A = 7x + 4 and  m ∠B = 4x+ 9.

Since  ∠A and  ∠B are complementary, they add upto 90.

m∠A +  m∠B  = 90

7x + 4 + 4x + 9 = 90

11x + 4 + 9 = 90

11x + 13 = 90

Subtracting 13 on both sides.

11x = 90 - 13

So, the required angles are 53 and 37.

Problem 4 :

The measure of an angle is 44 more than the measure of its supplement. Find the measures of the angles.

Let x be the required angle, its supplement be 180-x.

x = 180-x + 44

x = 224 - x

Add x on both sides.

x + x = 224

Divide by 2.

180 - x ==> 180 - 112 ==>  68

So, the required angles are 112 and 68.

Problem 5 :

What are the measures of two complementary angles if the difference in the measures of the two angles is 12.

Let x be a angle, its complementary angle is 90 - x.

x - (90 - x) = 12

x - 90 + x = 12

2x = 12 + 90

Dividing by 2 on both sides.

90 - 51 ==> 39

So, the required angles are 39 and 51.

Problem 6 :

Find the measures of two supplementary angles  ∠N and  ∠M if the measure of angle N is 5 less than 4 times the measure of angle M.

∠N = 4 ∠M - 5

∠N and  ∠M are supplementary.

∠N + ∠M = 180

4∠M - 5  + ∠M = 180

5 ∠M = 180 + 5

Dividing by 5

Applying the value of  ∠M, to find  ∠N.

∠N = 4(37) - 5

∠N = 148 - 5

Problem 7 :

Suppose  ∠T and  ∠U are complementary angles. Find x, i f  ∠T = 16x - 9 and  ∠U = 4x - 1.

Since  ∠T and  ∠U are complementary angles.

∠T +  ∠U = 90

16x - 9 + 4x - 1 = 90

20x - 10 = 90

Add 10 on both sides.

20x = 90 + 10

So, the required angles are 71 and 19.

Problem 8 :

Two angles are vertical in relation. One angle is 2y and the other angle is y + 130. Find each angle measure.

If two angles are vertical, then they will have the same measure.

2y = y + 130

2y - y = 130

2y = 260 and y + 130 = 260

So, those two angels are 260 and 260.

Problem 9 :

The measure of two supplementary angles are in the ratio 4 : 2, Find those two angles.

Let the required angles be 4x and 2x.

4x + 2x = 180

Divide by 6, we get

4x = 4(30) ==> 120

2x = 2(30) ==> 60

So, the required those two angles are 60 and 120.

• Variables and Expressions
• Variables and Expressions Worksheet
• Place Value of Number
• Formation of Large Numbers
• Laws of Exponents
• Angle Bisector Theorem
• Pre Algebra
• SAT Practice Topic Wise
• Geometry Topics
• SMO Past papers
• Parallel Lines and Angles
• Properties of Quadrilaterals
• Circles and Theorems
• Transformations of 2D Shapes
• Quadratic Equations and Functions
• Composition of Functions
• Polynomials
• Fractions Decimals and Percentage
• Customary Unit and Metric Unit
• Honors Geometry
• 8th grade worksheets
• Linear Equations
• Precalculus Worksheets
• 7th Grade Math Worksheets
• Vocabulary of Triangles and Special right triangles
• 6th Grade Math Topics
• STAAR Math Practice
• Math 1 EOC Review Worksheets
• 11 Plus Math Papers
• CA Foundation Papers
• Algebra 1 Worksheets

Recent Articles

Finding range of values inequality problems.

May 21, 24 08:51 PM

Solving Two Step Inequality Word Problems

May 21, 24 08:51 AM

Exponential Function Context and Data Modeling

May 20, 24 10:45 PM

© All rights reserved. intellectualmath.com

Beginning Algebra Tutorial 15

• Use Polya's four step process to solve word problems involving numbers, rectangles, supplementary angles, and complementary angles.

Whether you like it or not, whether you are going to be a mother, father, teacher, computer programmer, scientist, researcher, business owner, coach, mathematician, manager, doctor, lawyer, banker (the list can go on and on).  Some people think that you either can do it or you can't.  Contrary to that belief, it can be a learned trade.  Even the best athletes and musicians had some coaching along the way and lots of practice.  That's what it also takes to be good at problem solving.

George Polya , known as the father of modern problem solving, did extensive studies and wrote numerous mathematical papers and three books about problem solving.  I'm going to show you his method of problem solving to help step you through these problems.

If you follow these steps, it will help you become more successful in the world of problem solving.

Polya created his famous four-step process for problem solving, which is used all over to aid people in problem solving:

Step 1: Understand the problem.  

Step 2:   Devise a plan (translate).  

Step 3:   Carry out the plan (solve).  

Step 4:   Look back (check and interpret).  

Just read and translate it left to right to set up your equation .

Since we are looking for a number, we will let 

x = a number

*Get all the x terms on one side

*Inv. of sub. 2 is add 2  

FINAL ANSWER: 

We are looking for two numbers, and since we can write the one number in terms of another number, we will let

x = another number 

one number is 3 less than another number:

x - 3 = one number

*Inv. of sub 3 is add 3

*Inv. of mult. 2 is div. 2  

Another number is 87.

Perimeter of a rectangle = 2(length) + 2(width)

We are looking for the length and width of the rectangle.  Since length can be written in terms of width, we will let

length is 1 inch more than 3 times the width:

1 + 3 w = length

*Inv. of add. 2 is sub. 2

*Inv. of mult. by 8 is div. by 8  

FINAL ANSWER:

Length is 10 inches.

Complimentary angles sum up to be 90 degrees.

We are already given in the figure that

x = 1 angle

5 x = other angle

*Inv. of mult. by 6 is div. by 6

The two angles are 30 degrees and 150 degrees.

To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that  problem .  At the link you will find the answer as well as any steps that went into finding that answer.

  Practice Problems 1a - 1c: Solve the word problem.  

(answer/discussion to 1c)

http://www.purplemath.com/modules/ageprobs.htm This webpage goes through examples of age problems, which are like the numeric problems found on this page.

Go to Get Help Outside the Classroom found in Tutorial 1: How to Succeed in a Math Class for some more suggestions.

Last revised on July 26, 2011 by Kim Seward. All contents copyright (C) 2001 - 2010, WTAMU and Kim Seward. All rights reserved.

• Math Article

Supplementary Angles

Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°. Similarly, complementary angles add up to 90 degrees.  The two supplementary angles, if joined together, form a straight line and a straight angle.

But it should be noted that the two angles that are supplementary to each other, do not have to be next to each other. Hence, any two angles can be supplementary angles, if their sum is equal to 180°.

Geometry is one of the important branches of mathematics that deals with the study of different shapes. It initiates the study of lines and angles . A straight line is a line without curves and it is defined as the shortest distance between two points. An angle is formed when the line segment meets at a point.

What are Supplementary Angles?

In Maths, the meaning of supplementary is related to angles that make a straight angle together. It means, two angles are said to be supplementary angles when they add up to 180 degrees. Two angles are supplementary, if

• One of its angles is an acute angle and another angle is an obtuse angle.
• Both of the angles are right angles.

This means that ∠A + ∠B = 180° .

See the figure below for a better understanding of the pair of angles that are supplementary.

Examples of Supplementary Angles

Some of the examples of supplementary angles are:

• 120° + 60° = 180°
• 90° + 90° = 180°
• 140° + 40° = 180°
• 96° + 84° = 180°

Properties of Supplementary Angles

The important properties of supplementary angles are:

• The two angles are said to be supplementary angles when they add up to 180°.
• The two angles together make a straight line, but the angles need not be together.
• “ S ” of supplementary angles stands for the “ S traight” line. This means they form 180°.

Adjacent and Non-Adjacent Supplementary Angles

There are two types of supplementary angles:

• Adjacent supplementary angles
• Non-adjacent supplementary angles

Adjacent Supplementary angles

The supplementary angles that have a common arm and a common vertex are called adjacent supplementary angles. The adjacent supplementary angles share the common line segment and vertex with each other.

For example, the supplementary angles 110° and 70°, in the given figure, are adjacent to each other.

Non-adjacent Supplementary angles

The supplementary angles that do not have a common arm and a common vertex are called non-adjacent supplementary angles. The non-adjacent supplementary angles do not share the line segment or vertex with each other.

For example, the supplementary angles 130° and 50°,  in the given figure, are non-adjacent to each other.

How to Find Supplementary Angles?

As we know, if the sum of two angles is equal to 180°, then they are supplementary angles. Each of the angles is said to be a supplement of another angle. Hence, we can determine the supplement of an angle, by subtracting it from 180°.

For example, if you had given that two angles that form supplementary angles. If one angle is ∠A then another angle ∠B is its supplement.  Hence,

∠A = 180° – ∠B (or)

∠B = 180° – ∠A

Supplementary Angles Theorem

The supplementary angle theorem states that if two angles are supplementary to the same angle, then the two angles are said to be congruent.

If ∠x and ∠y are two different angles that are supplementary to a third angle ∠z, such that,

∠x + ∠z = 180 ……. (1)

∠y + ∠z = 180 ……. (2)

Then, from the above two equations, we can say,

Hence proved.

Supplementary and Complementary Angles

Both supplementary and complementary angles are pairs of angles, that sum up to 180° and 90°, respectively.  Let us find more differences between the pair of angles.

Video Lesson on Types of Angles

Related Articles

• Straight Angle
• Corresponding Angles
• Linear pairs of angles
• Alternate angles
• Vertically opposite angles

Problems and Solutions on Supplementary angles

Question 1:  Find the measure of an unknown angle from the given figure.

We know that the supplementary angles add up to 180 °.

X + 55° + 40° = 180°

X + 95° = 180°

X = 180°- 95°

Therefore, the unknown angle, X = 85°

Question 2: If ∠x and ∠y are supplementary angles and ∠x = 67, then find ∠y.

Solution: Given,  ∠x and ∠y are supplementary angles

Since, ∠x + ∠y = 180°

∠y = 180 – ∠x 

∠y = 180 – 67

Question 3: The two given angles are supplementary. If the estimate of the angle is two times the estimate of the other, what is the measure of each angle?

Assume the measure of one of the angles that are supplementary to be “a”.

The estimate of the angle is two times the estimate of the other.

The measure of the other angle is 2a.

If the total of the estimates of the given two angles is 180°, then the angles are termed supplementary.

The 2 supplementary angles are 60 and 120.

Question 4: The two angles P and Q are supplementary, find the angles given that

∠P = 2x + 15 and ∠Q = 5x – 38.

∠P + ∠Q = 180

It is given that ∠P = 2x + 15 and ∠Q = 5x – 38.

Substitute the values of P and Q respectively.

Question 5: What are the values of angles A and B if the value of angles A and B are supplementary in a way that angle A = 2x + 10 and angle B = 6x – 46?

∠A + ∠B = 180

(2x + 10) + (6x – 46) = 180

8x – 36 =180

x = 216 / 8

A = 2x + 10 and angle B = 6x – 46

Angle A = 2 (27) + 10 = 64

Angle B = 6 (27) – 46 = 116

Question 6: The given two angles are supplementary in nature. The estimates of the bigger angle are five times greater than four times the estimate of the lesser angle. Find the measure of the larger angle.

Assume the two angles supplementary angles to be x (bigger angle) and y (smaller angle).

According to the question,

(4y + 5) + y =180

5y + 5 =180

5y = 175 = 35

The bigger angle = x = 4 * (35) + 5 = 145

Question 7: The two supplementary angles are in the ratio three : two. What are the angles?

Assume the two supplementary angles to be 3x and 2x.

3x + 2x = 180

x = 180 / 5 = 36

The angle are 3x = 3 * 36 = 108 and

2x = 2 * 36 = 72

Therefore, the two supplementary angles are 108 and 72.

Practice Questions

• What is the supplement of angle 65 degrees?
• Are the angles 80 ° and 120 ° supplementary?
• Find the supplement of 140 °.

Frequently Asked Questions – FAQs

Can 2 acute angles be supplementary angles, can 2 obtuse angles be supplementary angles, can 2 right angles be supplementary angles, is supplementary and complementary angles same, what angle is formed if we put the supplementary angles together, complementary angles form what type of angle.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

Visit BYJU’S for all Maths related queries and study materials

Your result is as below

Request OTP on Voice Call

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.