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 **do not** have to be congruent or adjacent.

#### Example A

The two angles below are supplementary. If

Set up an equation. However, instead of equaling

#### Example B

What are the measures of two congruent, supplementary angles?

Supplementary angles add up to

#### Example C

Find the measure of an angle that is a supplementary to

Because supplementary angles have to add up to

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### Guided Practice

Find the measure of an angle that is supplementary to

45∘ 118∘ 32∘ 2∘

**Answers:**

180∘−45∘=135∘ .180∘−118∘=62∘ .180∘−32∘=148∘ .180∘−2∘=178∘ .

### Explore More

Find the measure of an angle that is supplementary to

114∘ 11∘ 91∘ 84∘ 57∘ x∘ (x+y)∘

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

- Name two supplementary angles.

- If
m∠INJ=63∘ , findm∠JNL .

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

- Supplementary angles add up to
180∘ .

For 11-12, find the value of

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 1.8.