Question

Triangle G E F is shown with its exterior angles. Line G F extends through point B. Line F E extends through point A. Line E G extends through point C. Angles F E G and E G F are congruent. Sides E F and G F are congruent. Angle E F G is 50 degrees.
What is the measure of ∠EGF?


°

What is the measure of ∠CGF?


°

Answer 1

∠EGF = 65°.

Reason: EF = GF so triangle EGF is isosceles with base angles FEG and EGF equal. Sum of angles gives 50 + 2x = 180 → x = 65.

∠CGF = 115°.

Reason: C lies on the extension of EG, so ∠CGF is the supplement of interior ∠EGF: 180 − 65 = 115.