9.4 Supplementary Angles
Learning Objectives
- I can identify supplementary angles are solve supplementary angle problems.
Introduction
What if you were given two angles of unknown size and were told they are supplementary? 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.
Guided Learning
Two angles are supplementary if they add up to . Supplementary angles do not have to be congruent or adjacent, next to each other.
A line can be extended from a shape to create supplementary angles. This creates an exterior angle, an angle formed when you extend a line from the side of a polygon. The angle inside the polygon is an interior angle. In this figure, the 60o angle is an interior angle. The 120o angle is an exterior angle. These angles are supplementary. They add up to 1800.
Example A
The two angles below are supplementary. If what is ?
Set up an equation. However, instead of equaling , now the sum is .
Example B
What are the measures of two congruent, supplementary angles?
Supplementary angles add up to . Congruent angles have the same measure. So, , which means two congruent, supplementary angles are right angles, or .
Example C
Find the measure of an angle that is a supplementary to if is .
Because supplementary angles have to add up to , the other angle must be .
Guided Practice
Find the measure of an angle that is supplementary to if is:
Check your work with a partner.
Solutions
1. Because supplementary angles have to add up to , the other angle must be .
2. Because supplementary angles have to add up to , the other angle must be .
3. Because supplementary angles have to add up to , the other angle must be .
4. Because supplementary angles have to add up to , the other angle must be.
Review
Adjacent
Items that are adjacent are immediately next to each other.
Exterior angles
An exterior angle is an angle formed when you extend a line from the side of a polygon.
Interior angles
The inside angles connecting the sides of the polygon are called interior angles.
Supplementary angles
Two angles that add up to 180o are called supplementary angles.