Answers to Evens 2) Definition of Bisector 4) Angle Addition Postulate 6) Midpoint Theorem 8) Segment Addition Postulate 10) 75 12) c) 90 14) RSZ = 18, NSZ = 54

2-4 Special Pairs of Angles Answers to Warm Ups 1) Midpoint Theorem 2) Angle Add. Post. 3) Angle Bisector Def. 4) Midpoint Definition 5) Segment Add. Post.

Types of Angles Complementary: Two angles whose sum is 90. Supplementary: Two angles whose sum is 180.

TOO Find the complement and supplement of each angle 1) 32° 2) 87° 1) 32° 2) 87° 3) 110° 4) g° Answers: 1) c = 58° s = 148° 2) c = 3° s = 93 ° 3) c = NONE s = 70° 4) c = (90 – g)° s = (180 – g)°

Vertical Angle Theorem 2 1 Vertical Angle Theorem 3 Angles 1 and 2 are supplements 1 + 2 = 180 (angle addition) Angles 2 and 3 are supplements 2 + 3 = 180 (angle addition) 1 + 2 = 2 + 3 (substitution) 1 = 3 (subtraction) Angles 1 and 3 are called vertical angles (opposite of each other). Theorem: Vertical angles are congruent

TOO If the measure of angle 1 is 40 and the measure of angle 2 is 30, find the other missing angles 110 30 3 40 2 4 40 1 6 5 30 110

Example The measure of a complement is 3 more than twice the measure of the angle. Find the measure of each angle. 1st: x 2nd: 2x + 3 x + 2x + 3 = 90 x = 29 2(29) + 3 = 61 Answers: 29 and 61 90 – 29 = 61

Homework Page 52 #1-33 Flash Cards Complements Supplements Vertical Angle Theorem