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.
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.
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.
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, .
Name one linear pair in the diagram below.
One example is and .
Watch this video for help with the Examples above.
1. What is ?
2. What is ?
3. If , find .
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 .