How to Find Complementary and Supplementary Angles? (+FREE Worksheet!)
![How to Find Complementary and Supplementary Angles? (+FREE Worksheet!)](https://www.effortlessmath.com/wp-content/uploads/2021/02/Complementary-and-supplementary-angles-512x240.png)
In this article, we will introduce you to the rules of complementary and supplementary angles and how to use them to find the value of a missing angle.
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Definition of the Complementary and supplementary angles
- Two angles with a sum of 90 degrees are called complementary angles.
- Two angles with a sum of 180 degrees are Supplementary angles.
![](https://www.effortlessmath.com/wp-content/uploads/2021/02/Complementary-angles.png)
![](https://www.effortlessmath.com/wp-content/uploads/2021/02/Supplementary-Angles.png)
Examples
Complementary and supplementary angles – Example 1:
Find the missing angle.
![](https://www.effortlessmath.com/wp-content/uploads/2021/02/exm.png)
Solution:
Notice that the two angles form a right angle. This means that the angles are complementary, and their sum is 90.
Then: \(18+x=90→x=90^\circ-18^\circ=72^\circ\) The missing angle is 72 degrees
Complementary and supplementary angles – Example 2:
Angles Q and S are supplementary. What is the measure of angle Q if angle S is 35 degrees?
Solution:
Q and S are supplementary \(→Q+S=180→Q+35=180→ Q =180-35=145\)
Complementary and supplementary angles – Example 3:
Find the missing angle.
![](https://www.effortlessmath.com/wp-content/uploads/2021/03/Complementary-and-supplementary-angles-Example1.jpg)
Solution:
Notice that two angles form a straight angle when together. This means that the angles are supplementary and have a sum of \(180^\circ\).
\(x+43=180→x=180-43=137^\circ\)
Complementary and supplementary angles – Example 4:
Find the missing angle.
![](https://www.effortlessmath.com/wp-content/uploads/2021/03/Complementary-and-supplementary-angles-Example2.jpg)
Solution:
Notice that two angles form a straight angle when together. This means that the angles are supplementary and have a sum of \(180^\circ\).
\(x+38=180→x=180-38=142^\circ\)
Exercises for Complementary and supplementary angles
Find the missing measurement in the pair of angles.
Find the missing measurement in the pair of angles.
1. \(\color{blue}{x=}\)
![](https://www.effortlessmath.com/wp-content/uploads/2021/03/Complementary-and-supplementary-angles-Example3.png)
2.\(\color{blue}{x=}\)
![](https://www.effortlessmath.com/wp-content/uploads/2021/03/Complementary-and-supplementary-angles-Example4.png)
3.\(\color{blue}{x=}\)
![](https://www.effortlessmath.com/wp-content/uploads/2021/03/Complementary-and-supplementary-angles-Example5.png)
4.\(\color{blue}{x=}\)
![](https://www.effortlessmath.com/wp-content/uploads/2021/03/Complementary-and-supplementary-angles-Example6.png)
5.The measure of an angle is \(31^°\). What is the measure of its complementary angle? __________
6.The measure of an angle is \(76^°\). What is the measure of its supplementary angle? __________
![](https://www.effortlessmath.com/wp-content/uploads/2019/12/answers.png)
- \(\color{blue}{156^\circ}\)
- \(\color{blue}{15^\circ}\)
- \(\color{blue}{113^\circ}\)
- \(\color{blue}{46^\circ}\)
- \(\color{blue}{59^\circ}\)
- \(\color{blue}{104^\circ}\)
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