Q:

The sum of the angle measures of a polygon with s sides is 2340. find s.

Accepted Solution

A:
s=15 
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 s sides (or angles),the sum of all the interior and exterior angles would be 180∘×sand sum of interior angles would be 180∘×n−360∘=180∘(s−2)As sum of angles is 2340∘Hence, 180(s−2)=2340 or s−2=2340180=13and s=13+2=15 and polygon is a Pentadecagon.i hope u understand :)