Question

an interior angle of a regular polygon has a measure of 108°. what type of polygon is it? the polygon is a decagon a hexagon an octagon a pentagon

Explanation:

Step1: Find the measure of an exterior angle

The sum of an interior angle and its corresponding exterior angle of a polygon is \(180^{\circ}\).
If the interior angle is \(108^{\circ}\), then the exterior angle \(e = 180^{\circ}- 108^{\circ}=72^{\circ}\)

Step2: Use the formula for the number of sides of a regular polygon

The sum of the exterior angles of any polygon is \(360^{\circ}\). For a regular polygon with \(n\) sides, \(n=\frac{360^{\circ}}{e}\) (where \(e\) is the measure of one exterior angle)
Substitute \(e = 72^{\circ}\) into the formula: \(n=\frac{360^{\circ}}{72^{\circ}} = 5\)

Answer:

a pentagon