If the measure of each interior angle of a regular polygon is 165, find the number of sides of the polygon.

If the interior angle of a regular polygon is 165°, then the size of its exterior angle is 15°. Since the exterior angles of a polygon always add to 360°, then the number of sides is 360/15 = 24.

There are 24 sides on this polygon. Answer is 24

There is an equation for this. You take 180°-165°=15°. Then you take 360:15=24. So there are 24 exterier angles with each angle being 15°. Since there are 24 exterior angles, there are 24 sides.