Question

The sum of the interior angles of s regular polygon is 3960, how many sides does it have?

Answer 1

The equation for the sum of interior angles is :

Sum = (n-2) x 180, where n is the number of sides.

Replace sum with the given sum:

3960 = (n-2) x 180

Divide both sides by 180:

22 = n-2

Add 2 to each side:

24 = n

It has 24 sides.

For Each interior angle, divide the total sum by the number of sides:

3960 / 24 = 165 degrees

The interior and exterior angle needs to equal 180 degrees. To find the exterior angle, subtract the interior angle from 180:

180 - 165 = 15 degrees.