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.
Identifying Linear Pairs
1. 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, .
2. Name one linear pair in the diagram below.
One example is and .
The following Examples use the diagram below:
What is ?
What is ?
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 .
To view the Review answers, open this PDF file and look for section 1.9.