Question

a figure is shown below. what is the measure of ∠g? o a 103° o b. 77° o c. 56° o d. 124°

Explanation:

Step1: Find the measure of ∠AFG

Use the linear - pair property. If an angle is \(124^{\circ}\), then \(\angle AFG = 180^{\circ}-124^{\circ}\)

$$ \angle AFG=56^{\circ} $$

Step2: 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. Here, \(\angle G\) is an exterior angle of the triangle. So \(\angle G=47^{\circ}+\angle AFG\)
Substitute \(\angle AFG = 56^{\circ}\) into the formula: \(\angle G=47^{\circ}+56^{\circ}\)

$$ \angle G = 103^{\circ} $$

Answer:

A. \(103^{\circ}\)