Question

what is the measure of ∠egf?
what is the measure of ∠cgf?

Explanation:

Step1: Analyze \(\triangle EGF\)

Since \(EG = FG\), \(\triangle EGF\) is isosceles. Let \(\angle EGF=\angle EFG\). The sum of angles in a triangle is \(180^{\circ}\). Given \(\angle GEF = 50^{\circ}\), then \(\angle EGF=\frac{180 - 50}{2}=65^{\circ}\).

Step2: Analyze \(\angle CGF\)

\(\angle CGF\) and \(\angle EGF\) are supplementary (they form a linear - pair). So \(\angle CGF=180^{\circ}-\angle EGF\). Substituting \(\angle EGF = 65^{\circ}\), we get \(\angle CGF=180 - 65=115^{\circ}\).

Answer:

1. \( 65^\circ \)
2. \( 115^\circ \)