Question

an isosceles triangle is shown. what is the measure of ∠f? a 32° b 58° c 64° d cannot be determined

Explanation:

Step1: Recall isosceles - triangle property

In an isosceles triangle, two angles are equal.

Step2: Recall sum of triangle angles

The sum of the interior angles of a triangle is 180°. Let the equal angles be $\angle E$ and $\angle F$. Given one angle is 58°.
If the 58° angle is the non - equal angle, then $\angle E=\angle F$. We use the formula $\angle E+\angle F + 58^{\circ}=180^{\circ}$. Substituting $\angle E=\angle F$, we get $2\angle F+58^{\circ}=180^{\circ}$.

Step3: Solve for $\angle F$

First, subtract 58° from both sides of the equation $2\angle F+58^{\circ}=180^{\circ}$: $2\angle F=180^{\circ}- 58^{\circ}=122^{\circ}$. Then divide both sides by 2: $\angle F = 61^{\circ}$. But this is not in the options.
If the 58° angle is one of the equal angles, then $\angle F = 58^{\circ}$.

Answer:

B. 58°