# How do you find the sum of the interior angle measures of a convex 16 gon?

##### 2 Answers

Sum of interior angles of a convex 16 sided-polygon

( **hexakaidecagon** ) would be

#### Explanation:

Whatever the number of sides of a polygon,

the sum of its exterior angles is always

Further, each pair of exterior angle and interior angle adds up to

Hence in a polygon with

the sum of all the interior and exterior angles would be

and sum of interior angles would be

Hence sum of interior angles of a convex 16-sided polygon would be

Any polygon can be broken up into triangles by drawing in all the possible diagonals from one vertex.

You will find that the number of triangles is always 2 less than the number of sides.

The sum of the angles in any triangle is

Consider the following: