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

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### Guidance

Two angles are **adjacent** if they have the same vertex, share a side, and do not overlap 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 (add up to ). and are a linear pair.

#### Example A

What is the measure of each angle?

These two angles are a linear pair, so they add up to .

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. They are supplementary because they add up to : .

#### Example C

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

Because linear pairs have to add up to , the other angle must be .

### Guided Practice

Use the diagram below. Note that .

1. Name one linear pair of angles.

2. What is ?

3. What is ?

4. If , find .

**Answers:**

1. and

2.

3.

4.

### 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.

For exercise 6, find the value of .

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