Question

What is the measure of ∠EGF? What is the measure of ∠CGF?

Answer 1

measure of ∠EGF = 1/2( 180 - 50)
= 1/2(130)
= 65

the measure of ∠CGF = 180 - 65
= 115

Answer 2

Hello!

This is an isosceles triangle, which means its base angles are congruent. Interior angles of triangle add to equal 180 degrees, so you can make an equation to solve for the measure of the base angles. I'll call the base angles x.

180 = 50 + 2x
130 = 2x
65 = x

That gives you m∠EGF and m∠FGE (65°).

To find m∠CGF, you must know that it and ∠EGF are supplementary (they add to equal 180 degrees). Make another equation setting them to equal 180 using m∠EGF (65°):

180 = 65 + x
115 = x

Answer:
m∠EGF = 65°
m∠CGF = 115°