1. 2.2 Complementary and Supplementary Angles

2. Definition: Complementary Angles are two angles whose measures sum to 90.
Each of the two angles is called the complement of the other.

3. Adjacent Angles
Definition: Two angles are called adjacent angles if they share a vertex and a common side.
Angles 1 and 2 are adjacent: 1 2

4. Examples of Complementary Angles
Adjacent Angles
Non-Adjacent Angles

5. Definition: Supplementary Angles are two angles whose measures sum to 180.
Each of the two angles is called the supplement of the other.

6. Examples of Supplementary Angles
Adjacent Angles
Non-Adjacent Angles

7. Algebra & Angle Relationships
You can find the complement of an angle that measures x° by subtracting its measure from 90°, or (90 – x)°.
You can find the supplement of an angle that measures x° by subtracting its measure from 180°, or (180 – x)°.

8. Example: Finding the Measures of Complements and Supplements
Find the measure of each of the following.
A. complement of F
(90 – x)
90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)

9. Another Example
Find the measure of each of the following.
a. complement of E
(90 – x)°
90° – (7x – 12)° = 90° – 7x° + 12°
= (102 – 7x)°
b. supplement of F
(180 – x)
180 – 116.5° =

10. Verbal Description of Angle Relationships
An angle is 10° more than 3 times the measure of its complement. Find the measure of the complement.
Step 1 Let mA = x°.
Then B, its complement measures (90 – x)°.
Step 2 Write and solve an equation.
x = 3(90 – x) + 10
Substitute x for mA and 90 – x for mB.
x = 270 – 3x + 10
Distrib. Prop.
x = 280 – 3x
Combine like terms.
4x = 280
Divide both sides by 4.
x = 70
Simplify.
The measure of the complement, B, is (90 – 70) = 20.

11. Verbal Description of Angle Relationships
An angle’s measure is 12° more than half the measure of its supplement. Find the measure of the angle.
Substitute x for mA and x for mB.
x = 0.5(180 – x) + 12
x = 90 – 0.5x + 12
Distrib. Prop.
x = 102 – 0.5x
Combine like terms.
1.5x = 102
Divide both sides by 1.5.
x = 68
Simplify.
The measure of the angle is 68.

12. Verbal Description of Angle Relationships
Two angles are complementary.
The angle measures are in the ratio 7:8.
Find the measure of each angle.
Solution: The angle measures can be represented by 7x and 8x. Then