1. In the diagram below, AB and CD intersect at E, (m) Angle AEC = 6x -20 and the (m) Angle BED is 4x + 10. Find the value of x. (6x -20) (4x + 10) A E B D C

2. Answer Special Angle Relationship Property: Vertical Angles Therefore, 6x-20 = 4x+10 +20 = +20 6x = 4x +30 -4x = -4x 2x = 30 x = 15

3. Theorems involving Pairs of Angles Thm: 4.3 If two angles are complements of the same angle, then they are congruent. Thm: 4.4 If two angles are congruent, then their complements are congruent. Thm: 4.5 If two angles are supplements of the same angle, then they are congruent. Thm: 4.6 If two angles are congruent, then their supplements are congruent.