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 32˚ 58˚ B

Definitions Supplementary angles – the sum of their measures is 180˚ Each angle is the supplement of the other 46˚ D 134˚ C

Identify Complements and Supplements 158˚ 22˚ 15˚ 85˚ 55˚ 35˚

Definitions Adjacent angles – have a common vertex and side, but no common interior points Common side B Common vertex

Identify Adjacent Angles 3 4 5 6 1 2

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 1 2 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 2 3 1

Use Theorems 7 and 8 are supplementary 8 and 9 are supplementary Name a pair of congruent angles. 7 9 8 7 9

Guided Practice Pg. 70 #1-7