Question

find the measure of ∠f.

Explanation:

Step1: Identify Exterior Angle Property

The exterior angle of a triangle equals the sum of the two non - adjacent interior angles. Here, the exterior angle at \(G\) (with measure \(58^{\circ}\)) is equal to the sum of \(\angle E\) and \(\angle F\). Given that \(\angle E=x^{\circ}\) and \(\angle F = x^{\circ}\), so we have the equation \(58=x + x\).

Step2: Solve for \(x\)

Simplify the right - hand side of the equation: \(58 = 2x\). Then divide both sides by 2: \(x=\frac{58}{2}=29\). So the measure of \(\angle F\) is \(29^{\circ}\).

Answer:

\(29^{\circ}\)