Question

m∠f
80
58°

Explanation:

Step1: Use the exterior - angle property of a triangle

The exterior - angle property 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.
Here, \(\angle EGH\) is an exterior angle of \(\triangle EFG\). So, \(m\angle EGH=m\angle F + m\angle E\) (where \(m\angle E = x^{\circ}\) and \(m\angle F=x^{\circ}\)).
We know that \(m\angle EGH = 58^{\circ}\).
So, \(58^{\circ}=x^{\circ}+x^{\circ}\).

Step2: Solve the equation for \(x\)

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

Answer:

\(m\angle F=29^{\circ}\)