Question

If an interior angle of a regular polygon measures 108°, how many sides does the polygon have?

Answer 1

5 sides

Explanation:

Use the formula for the measure of an interior angle of a polygon

`((n - 2)180)/(n)`

Solve for n (the number of sides):

108 =
`((n - 2)180)/(n)`

108n = (n - 2)180

108n = 180n - 360

-72n = -360

n = 5

So, the polygon has 5 sides.

Answer 2

5

Explanation:

(n-2)180 = 108

n

Distribute

180n-360=108n

-360=-72n

5=n

n=5