Question

Is it possible to have a regular polygon each of whose interior angles is ${100}^o$?

Answer 1

We know that sum of interior angles of a regular polygon is ${360}^o$
As we know that the sum of interior and exterior angles is ${180}^o$

Exterior angle $+$ interior angle $={180}^o$

Exterior angle$=$ $180-$ Interior angle

Exterior angle $=180-{100}^o={80}^o$

When we divide the exterior angle we will get the number of exterior angles, since it is a regular polygon so number of exterior angles is equal to number of sides.

Therefore $n={360}^o/{80}^o=4.5$

And we know that $4.5$ is not a integer so it is not possible to have a regular polygon whose exterior angle is ${100}^o$