# What is the sum, in degrees, of the measures of the interior angles of a pentagon?

##### 1 Answer

Jan 3, 2017

#### Explanation:

In any

This can be proven by taking a regular n-gon (why not?), and drawing a (isosceles) triangle from the centre to one of the sides.

The centre angle will be

The inner angle of the n-gon will be just twice that, or

The sum of all inner angles will then be:

In case of a regular n-gon, each angle will be