Question

how many sides does a regular polygon have if each of its interior angles is 165°

Answer 1

Given Interior angle = 165.

The measure of each exterior angle = 180 - 165

                                                             = 15


We know that sum of each exterior angles = 360

                                                                        = 360/15

                                                                        = 24.


Therefore the number of sides = 24.


Hope this helps!

Answer 2

Answer:

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