Here is an easy way to solve the problem:
1) The interior and the exterior angles
make a linear pair: add up to make 180°.
180° - 165° = 15° measure of one ext. angle
2) the sum of the exterior angles of any convex polygon is 360°
360° ÷ 15° = 24 exterior angles
3) the number of exterior angles = the number of interior angles = the number of sides in any convex polygon
4) Therefor there are 24 sides in this regular polygon