Question

each exterior angle of a regular polygon measures 18°. how many sides does the polygon have?
a. 8
b. 18
c. 12
d. 20

Explanation:

Step1: Recall exterior - angle formula

The sum of exterior angles of any polygon is 360°. For a regular polygon, if the measure of each exterior angle is \(x\) and the number of sides is \(n\), then \(n=\frac{360^{\circ}}{x}\).

Step2: Substitute the given value

Given \(x = 18^{\circ}\), we substitute it into the formula \(n=\frac{360^{\circ}}{18^{\circ}}\).
\[n=\frac{360}{18}=20\]

Answer:

D. 20