Question

One exterior angle of a regular polygon measures 30. What is the sum of the polygon's interior angle measures?

Answer 1

The explanation with the solution is given below.

Explanation:

Exterior angle of `n` sided regular polygon is found by the formula

`360/n`

We are given one exterior angle is `30^o`

`360/n = 30`

`=>n = 360/30`

`=> n=12`

The polygon is a dodecagon.

The sum of the interior angles is found by the formula

`(n-2)*180^o`

Here we found the number of sides is 12, therefore `n=12`

`(12-2)*180^o`

`=10*180^o`

`=1800^o` Answer