Question

if a regular polygon has exterior angles that measure 36° each, how many sides does the polygon have?
a. 8
b. 10
c. 12
d. 6

Explanation:

Step1: Recall exterior - angle formula

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

Step2: Solve for \(n\)

We know that \(\theta = 36^{\circ}\), and \(\theta=\frac{360^{\circ}}{n}\). So, \(n=\frac{360^{\circ}}{\theta}\). Substituting \(\theta = 36^{\circ}\) into the formula, we get \(n=\frac{360}{36}=10\).

Answer:

B. 10