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

#### Risposta:

Sum of interior angles of a convex 16 sided-polygon

( hexakaidecagon ) would be 2520^@.

#### Spiegazione:

Whatever the number of sides of a polygon,

the sum of its exterior angles is always 360^@

Further, each pair of exterior angle and interior angle adds up to 180^@

Hence in a polygon with n sides (or angles),

the sum of all the interior and exterior angles would be 180^@xxn

and sum of interior angles would be 180^@xxn-360^@=180^@(n-2)

Hence sum of interior angles of a convex 16-sided polygon would be 180^@xx(16-2)=180^@xx14=2520^@.