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

Question

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°

Answer 1

To find the measure of ∠HCF, we can use the fact that line AE and line DF are parallel, so ∠ABG and ∠HCF are corresponding angles.

Since ∠ABG = 12x and ∠HCF = 11x + 9, we can set up an equation:

12x = 11x + 9
12x - 11x = 9
x = 9

Now that we have found the value of x, we can substitute it back into the expression for ∠HCF:

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

Therefore, the measure of ∠HCF is 108°.

So the answer is 108°.