Question

How to find the measure of angle FGC If segments AC and BD are parallel and they are cut by the transversal FE

Answer 1

Angles FGC and FHD are equal by the Corresponding Angles Theorem.

Make them equal to each other in an equation.
3x - 9 = 2x + 1
Add 9 to both sides.

3x = 2x + 10
Subtract 2x from both sides.

x = 10

Plug in 10 for x in the expression for angle FGC, 3x - 9.
3(10) - 9
30 - 9 = 21

∠FGC = 21°.