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.
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?
For Examples 1 and 2, use the diagram below. Note that .
Name one linear pair of angles.
What is ?
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.
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 : .
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 .
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:
To see the Review answers, open this PDF file and look for section 1.9.