Question

review part 2 of 2 the measure of an exterior angle of a regular polygon is given below. find the measure of an interior angle. then find the number of sides. 15 what is the measure of an interior angle? 165 how many sides does the polygon have? \square

Explanation:

Step1: Recall exterior-interior angle relation

An interior angle and its corresponding exterior angle of a regular polygon are supplementary, so \( \text{Interior Angle} + \text{Exterior Angle} = 180^\circ \). Given exterior angle is \( 15^\circ \), so interior angle is \( 180 - 15 = 165^\circ \) (already verified, now find number of sides).

Step2: Use sum of exterior angles

The sum of exterior angles of any polygon is \( 360^\circ \). For a regular polygon, \( \text{Number of Sides} = \frac{360^\circ}{\text{Measure of one exterior angle}} \). Substituting exterior angle \( 15^\circ \), we get \( \frac{360}{15} = 24 \).

Answer:

The measure of an interior angle is \( 165^\circ \), and the polygon has 24 sides.