Line AE and line DF are parallel. If m∠ABG = 12x and m∠HCF = 11x + 9, what is m∠HCF? points B and C are on line GH between points G and H, line AE intersects with line GH at point B, line DF intersects with line GH at point C 15° 72° 108° 112°

∠HCF = 108°

Option C is correct.

Step-by-step explanation:

The diagram of the lines AE, DF and GH is presented in the attached image.

∠ABG = 12x

∠HCF = (11x + 9)

From the diagram, it is evident that

∠ABG = ∠EBC = 12x (opposite angles are equal)

∠HCF = ∠DCB = (11x + 9) (opposite angles are equal)

Then ∠EBC = ∠DCB

Hence, from the image, it is evident that

12x = 11x + 9

x = 9

∠HCF = 11x + 9 = 11(9) + 9 = 99 + 9 = 108°

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