Question

a regular polygon is drawn in a circle so that each vertex is on the circle and is connected to the center by a radius. each of the central angles has a measure of 40°. how many sides does the polygon have?
8
9
10
12

Explanation:

Step1: Recall the total central - angle property

The sum of the central angles of a circle is 360°.

Step2: Calculate the number of sides

Let \(n\) be the number of sides of the regular polygon. Since the measure of each central angle is 40°, and the sum of central angles is 360°, we use the formula \(n=\frac{360^{\circ}}{\text{measure of each central angle}}\). So \(n = \frac{360}{40}=9\).

Answer:

B. 9