# How to Find Complementary and Supplementary Angles? (+FREE Worksheet!)

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.

## 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.

## Examples

### Complementary and supplementary angles – Example 1:

Find the missing angle.

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.

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.

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. $$\color{blue}{x=}$$

2.$$\color{blue}{x=}$$

3.$$\color{blue}{x=}$$

4.$$\color{blue}{x=}$$

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? __________

1. $$\color{blue}{156^\circ}$$
2. $$\color{blue}{15^\circ}$$
3. $$\color{blue}{113^\circ}$$
4. $$\color{blue}{46^\circ}$$
5. $$\color{blue}{59^\circ}$$
6. $$\color{blue}{104^\circ}$$

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