### Supplementary Angles

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

What if you were given two angles of unknown size and were told they are supplementary? How would you determine their angle measures?

### Examples

#### Example 1

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

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#### Example 2

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

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#### Example 3

The two angles below are supplementary. If what is ?

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

#### Example 4

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 5

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 .

### Review

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 .

### Review (Answers)

To see the Review answers, open this PDF file and look for section 1.8.

### Resources