Question

question 7 of 10 each exterior angle of a regular polygon measures 30°. how many sides does the polygon have? a. 12 b. 15 c. 10 d. 11

Explanation:

Step1: Recall exterior - angle formula

The sum of exterior angles of any polygon is 360°. For a regular polygon with \(n\) sides, each exterior angle \(\theta=\frac{360^{\circ}}{n}\).

Step2: Solve for \(n\)

Given \(\theta = 30^{\circ}\), we have \(n=\frac{360^{\circ}}{\theta}\). Substituting \(\theta = 30^{\circ}\) into the formula, we get \(n=\frac{360^{\circ}}{30^{\circ}} = 12\).

Answer:

A. 12