Question

find the measure of \\( \angle f \\).

Explanation:

Step1: Use the exterior - angle property of a triangle

The exterior - angle property of a triangle states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
In triangle \(EFG\), \(\angle EGH\) is an exterior angle. So, \(\angle EGH=\angle F + \angle E\).
Given \(\angle EGH = 58^{\circ}\), \(\angle E=x^{\circ}\), and \(\angle F=x^{\circ}\). Then \(58=x + x\).

Step2: Solve the equation for \(x\)

Combine like terms: \(58 = 2x\).
Divide both sides of the equation by \(2\): \(x=\frac{58}{2}\).
\(x = 29\).

Answer:

\(29\)