geometry (please explain)

Question

 and  are parallel. If m∠ABG = 12x and m∠HCF = 11x + 9, what is m∠HCF?

 A. 15°

 B. 72° 

C. 108°

 D. 112°

Answer 1

As ∠ABG and ∠HCF are alternate exterior angles, they will have the same angle measure, which means we can set them equal to each other and solve for x:

m∠ABG = m∠HCF

12x = 11x+9

x = 9

Thus, m∠HCF = 11x + 9 = 11(9) + 9 = 99 + 9 = 108° (Option C)