Question

the exterior angle of a regular polygon is one third its interior angle. how many sides does the polygon has?

Answer 1

Let x be the exterior angle, Then the interior angle be 3x.

We know that Their sum = 180.

                                x + 3x = 180

                                    4x = 180

                                       x = 45.

We know that the Sum of exterior angles of a polygon = 360.

It will be 360/45 = 8.

The polygon has 8 number of sides.


Hope this helps!