Question

a regular polygon has an exterior angle measuring 30°. how many sides does the polygon have?
a. 8
b. 12
c. 14
d. 10

Explanation:

Step1: Recall the formula for the measure of an exterior angle of a regular polygon

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

Step2: Solve for \(n\)

Given \(\theta = 30^{\circ}\), we substitute into the formula \(n=\frac{360^{\circ}}{\theta}\)

Substitute \(\theta = 30^{\circ}\) into \(n=\frac{360^{\circ}}{\theta}\), we get \(n=\frac{360^{\circ}}{30^{\circ}}=12\)

Answer:

B. 12