6) AEB + BEC + DEC = 180
70 + BEC + 30 = 180
BEC + 100 = 180
BEC = 80°
7) ∠2 ≅ ∠4 because they are vertical angles
∠2 = ∠4 definition of congruency
88° = ∠4 substitution
8) complement means their sum equals 90°
20° + x = 90°
x = 70°
9) AEB + BED = 180 because they are a linear pair
AEB + 120 = 180
AEB = 60°
10) ∠2 + ∠3 = 180 because they are a linear pair
5x + 10 + x + 50 = 180 substitution
6x + 60 = 180 simplify (add like terms)
6x = 120 subtraction property of equality
x = 20 division property of equality
11) ∠1 ≅ ∠3 because they are vertical angles
∠1 = ∠3 definition of congruency
3x - 40 = x + 10 substitution
2x - 40 = 10 subtraction property of equality
2x = 50 addition property of equality
x = 25 division property of equality
12) AEB + CEB + CED = 180 supplementary angles
4x + 9x + 2x = 180 substitution
15x = 180 simplify (add like terms)
x = 12 division property of equality
CED = 2x = 2(12) = 24°
13) complement means their sum equals 90°
x + complement = 90°
complement = 90° - x
14) supplement means their sum equals 180°
5x + 30° + supplement = 180°
5x + supplement = 150°
supplement = (150 - 5x)°
15) x + 8x = 180
9x = 180
x = 20
8x = 8(20) = 160°