What if you were given two supplementary angles? How would you determine their angle measures? After completing this Concept, you'll be able to use the definition of supplementary angles to solve problems like this one.
Two angles are supplementary when they add up to . Supplementary angles do not have to be congruent or touching.
The two angles below are supplementary. If what is ?
Set up an equation.
What are the measures of two congruent, supplementary angles?
Supplementary angles add up to . Congruent angles have the same measure. Divide by 2, to find the measure of each angle.
So, two congruent, supplementary angles are right angles, or .
Name one pair of supplementary angles in the diagram below.
One example is and .
Watch this video for help with the Examples above.
Two angles are supplementary when they add up to .
Find the measure of an angle that is supplementary to if is
Find the measure of an angle that is supplementary to if is:
Use the diagram below for exercises 8-9. Note that .
- Name another pair of supplementary angles.
- If , find .
For exercises 10-13, determine if the statement is true or false.
- Supplementary angles add up to .
- Two angles on a straight line are supplementary angles.
- To be supplementary, two angles must be touching.
- It's possible for two angles in a triangle to be supplementary.
For 14-15, find the value of .