Question

If the measure of one interior angle of a regular polygon is 144 find the number of sides

Answer 1

(n - 2)180/n = interior angle

(n - 2)180/n= 144

(n - 2)180 = 144n

180n - 360 = 144n

180n - 144n = 360

36n = 360

n = 360/36

n = 10

Number of side is 1

Explanation:

Answer 2

The total degrees of any regular polygon can be defined as 180(n - 2) where
n = the number of sides of the of the polygon. Since each angle in a regular polygon is equal in measure, you could then find the measure of each angle by dividing the total degree measure by the number of sides.

In this problem, let's set up the following equation:

`(180(n-2))/(n) =144` where n = the number of sides of the regular polygon.

Solving this equation, we find n = 10 So we have a 10 sided polygon.