Question

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

Explanation:

Step1: Recall exterior - angle formula

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

Step2: Solve for \(n\)

We know that \(\theta = 30^{\circ}\), so \(n=\frac{360^{\circ}}{\theta}\). Substituting \(\theta = 30^{\circ}\) into the formula, we get \(n=\frac{360}{30}=12\).

Answer:

B. 12