What if you were given two angles of unknown size and were told they are supplementary? How would you determine their angle measures? After completing this Concept, you'll be able to use the definition of supplementary angles to solve problems like this one.

### Watch This

CK-12 Basic Geometric Definitions

Watch this video beginning at around the 3:20 mark.

James Sousa: Angle Basics--Supplementary Angles

Then watch the second part of this video.

James Sousa: Supplementary Angles

### Guidance

Two angles are
**
supplementary
**
if they add up to
. Supplementary angles
**
do not
**
have to be
*
congruent
*
or
*
next to each other
*
.

#### Example A

The two angles below are supplementary. If what is ?

Set up an equation. However, instead of equaling , now the sum is .

#### Example B

What are the measures of two congruent, supplementary angles?

Supplementary angles add up to . Congruent angles have the same measure. So, , which means two congruent, supplementary angles are right angles, or .

#### Example C

Find the measure of an angle that is a supplementary to if is .

Because supplementary angles have to add up to , the other angle must be .

### Guided Practice

Find the measure of an angle that is supplementary to if is:

**
Answers:
**

1. Because supplementary angles have to add up to , the other angle must be .

2. Because supplementary angles have to add up to , the other angle must be .

3. Because supplementary angles have to add up to , the other angle must be .

4. Because supplementary angles have to add up to , the other angle must be .

### Practice

Find the measure of an angle that is supplementary to if is:

Use the diagram below for exercises 8-9. Note that .

- Name two supplementary angles.

- If , find .

For exercise 10, determine if the statement is true or false.

- Supplementary angles add up to

For 11-12, find the value of .