Answer/Step-by-step explanation:
Part A:
(6x + 2)° + (8x + 6)° + (7x + 4)° = 180° (angles in a straight line)
Solve for x
6x + 2 + 8x + 6 + 7x + 4 = 180
Add like terms
21x + 12 = 180
21x + 12 - 12 = 180 - 12
21x = 168
21x/21 = 168/21
x = 8
Part B:
Method 1:
m<CFD + m<CFB + m<BFA = 180° (Angles in a straight line)
m<CFD + (6x + 2)° + (8x + 6)° = 180° (substitution)
Plug in the value of x
m<CFD + 6(8) + 2 + 8(8) + 6 = 180
m<CFD + 48 + 2 + 64 + 6 = 180
m<CFD + 120 = 180
m<CFD + 120 - 120 = 180 - 120
m<CFD = 60°
Method 2:
m<CFD = m<AFE (vertical angles are congruent)
m<CFD = (7x + 4)° (substitution)
Plug in the value of x
m<CFD = 7(8) + 4
m<CFD = 60°
