Question

find the measure of ∠f.

Explanation:

Step1: Find ∠EG F

Since ∠H G E is \(58^\circ\) and they are supplementary (linear pair), \(\angle EGF = 180^\circ - 58^\circ = 122^\circ\).

Step2: Analyze triangle EGF

Triangle EGF is isosceles (EG = FG, marked with ticks), so \(\angle E=\angle F\). Let \(\angle F = x\).

Step3: Use triangle angle sum

Sum of angles in a triangle is \(180^\circ\), so \(x + x + 122^\circ = 180^\circ\).
Simplify: \(2x = 180^\circ - 122^\circ = 58^\circ\).
Then \(x=\frac{58^\circ}{2}=29^\circ\).

Answer:

\(29^\circ\)