42.5k views
5 votes
the interior angles of a regular polygon each measures 165 degrees. how many sides does the polygon have

User Bfcm
by
6.6k points

1 Answer

1 vote
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
User Serhat
by
6.6k points