Question

1. choose the correct answer. use the polygon exterior angle sum theorem to find the measure of each of the exterior angles of the regular pentagon. 360° 108° 72° 180°

Explanation:

Step1: Recall the Polygon Exterior Angle Sum Theorem

The sum of the exterior angles of any polygon is \(360^{\circ}\).

Step2: Divide the sum by the number of sides

A pentagon has \(n = 5\) sides. Let \(x\) be the measure of each exterior angle. Using the formula \(x=\frac{360^{\circ}}{n}\), substitute \(n = 5\). So \(x=\frac{360^{\circ}}{5}\).

Step3: Calculate the value

\(\frac{360^{\circ}}{5}=72^{\circ}\)

Answer:

\(72^{\circ}\) (the third option)