Question

an exterior angle of a regular convex polygon is 40°. what is the number of sides of the polygon?
a. 8
b. 9
c. 10
d. 11

Explanation:

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

The sum of the exterior angles of any convex 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 \(\theta = 40^{\circ}\), we substitute into the formula \(\theta=\frac{360^{\circ}}{n}\). Then \(n=\frac{360^{\circ}}{\theta}\)

Substitute \(\theta = 40^{\circ}\) into \(n=\frac{360^{\circ}}{\theta}\), we get \(n=\frac{360}{40}=9\)

Answer:

B. 9