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.

### Watch This

### Guidance

Two angles are **adjacent** if they have the same vertex, share a side, and do not overlap

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

#### Example A

What is the measure of each angle?

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

Plug in

#### Example B

Are

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

Because linear pairs have to add up to

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### Guided Practice

Use the diagram below. Note that

1. Name one linear pair of angles.

2. What is

3. What is

4. If

**Answers:**

1.

2.

3.

4.

### Explore More

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

61∘ 23∘ 114∘ 7∘ 179∘ z∘

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 1.9.