Question

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

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem 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 \(\triangle EGF\), \(\angle EGH\) is an exterior angle. So, \(\angle EGH=\angle E+\angle F\).

Step2: Substitute the known values

Let \(\angle E = x^{\circ}\) and \(\angle F=x^{\circ}\), and \(\angle EGH = 58^{\circ}\). Then \(58^{\circ}=x^{\circ}+x^{\circ}\).

Step3: Solve the equation

Combine like terms: \(58^{\circ}=2x^{\circ}\). Divide both sides by 2: \(x = 29\).

Answer:

\(29^{\circ}\)