Question

A regular polygon is drawn in a cide so that each vertex is on the chce 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
10

Answer 1

9

Explanation:

The number of central angles in a regular polygon is always equal to the number of sides of the polygon.

Therefore, we have:

`n` = number of central angles

`N=` number of sides in the polygon

So

`N=n`

We also know that the sum of the central angles in a polygon must be 360 degreeso, so we have:

`n\theta = 360^(\circ)`

where

`\theta` = measure of each central angle

Here we are told that

`\theta=40^(\circ)`

So we can find the number of central angles:

`n=(360)/(\theta)=(360)/(40)=9`

So, the polygon has 9 sides:

`N=n=9`