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.

## Related Topics

- Special Right Triangles
- How to Solve Triangles Problems
- How to Find Volume and Surface Area of Cubes
- How to Calculate Cylinder Volume and Surface Area
- How to Solve Parallel Lines and Transversals Problems

## 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? *__________*

- \(\color{blue}{156^\circ}\)
- \(\color{blue}{15^\circ}\)
- \(\color{blue}{113^\circ}\)
- \(\color{blue}{46^\circ}\)
- \(\color{blue}{59^\circ}\)
- \(\color{blue}{104^\circ}\)