2.3 Complementary and Supplementary Angles

Definitions

• Complementary angles – the sum of their measures is 90˚– Each angle is the compliment of the other

A

B

32˚

58˚

Definitions

• Supplementary angles – the sum of their measures is 180˚– Each angle is the supplement of the other

134˚

46˚

C

D

Identify Complements and Supplements

22˚ 158˚

85˚

15˚

55˚35˚

Definitions

• Adjacent angles – have a common vertex and side, but no common interior points

B

Common side

Common vertex

Identify Adjacent Angles

12

43

65

Measures

• m A is a complement of C, and m A = 47˚. Find m C.– 43˚

• M P is a supplement of R, and m R = 36˚. Find m P.– 144˚

Definitions

• Theorem – a true statement that follows from other true statements

Theorem 2.1 Congruent Compliments Theorem

• If two angles are complementary to the same angle, then they are congruent

• m 1 + m 2 = 90˚• m 3 + m 2 =90˚• Then 1 3

12

3

Theorem 2.2 Congruent Supplements Theorem

• If two angles are supplementary to the same angle, then they are congruent

• m 1 + m 2 = 180˚• m 3 + m 2 = 180˚• Then 1 3 1

23

Use Theorems

• 7 and 8 are supplementary• 8 and 9 are supplementary• Name a pair of

congruent angles.– 7 9

79

8

Guided Practice

• Pg. 70 #1-7