Question

How many sides does a regular polygon have whose interior and exterior angles are in the ratio of 3:2?

Answer 1

Hello friend...

Let there are n sides of that polygon.

While the ratio is 7:2 and given that interior + exterior angles = 180 deg , then (7+2)*x = 180 => x=20.

It means that interior angle is 7*20= 140 deg and exterior 40 deg, which is also the central angle of the polygon.

Then 360 deg : 40 deg = 9 sides.

Hope this helps you...