What if you notice two angles in a picture that make a straight line? What information does this give you about the angles? After completing this Concept, you'll be able to apply the properties of linear pairs to help you solve problems.

### Watch This

CK-12 Foundation: Chapter1Linear PairsA

### Guidance

**Adjacent angles** are two angles that have the same vertex, share a side, and do not overlap. In the picture below, and are adjacent.

A **linear pair** is two angles that are adjacent and whose non-common sides form a straight line. If two angles are a linear pair, then they are supplementary.

and are a linear pair.

#### Example A

What is the value of each angle?

These two angles are a linear pair, so they are supplementary, or add up to . Write an equation.

So, plug in to get the measure of each angle.

#### Example B

Are and a linear pair? Are they supplementary?

The two angles are not a linear pair because they do not have the same vertex. However, they are supplementary, .

#### Example C

Name one linear pair in the diagram below.

One example is and .

Watch this video for help with the Examples above.

CK-12 Foundation: Chapter1LinearPairsB

### Vocabulary

** Adjacent angles** are two angles that have the same vertex, share a side, and do not overlap. A

**is two angles that are adjacent and whose non-common sides form a straight line. If two angles are a linear pair, then they are**

*linear pair***.**

*supplementary*### Guided Practice

1. What is ?

2. What is ?

3. If , find .

**Answers:**

1.

2.

3.

### Interactive Practice

### Practice

For 1-5, determine if the statement is true or false.

- Linear pairs are congruent.
- Adjacent angles share a vertex.
- Adjacent angles overlap.
- Linear pairs are supplementary.
- Supplementary angles form linear pairs.

Find the measure of an angle that forms a linear pair with if is:

For 12-16, find the value of .