Question

Is it possible to have a regular polygon each of whose exterior angles is ${50}^o$?

Answer 1

We know that sum of exterior angles of a regular polygon is ${360}^o$
Formula for exterior angle $=\frac{{360}^o}{n}$ where $n$ is the number of sides.

$⟹n=\frac{{360}^o}{{50}^o}=7.2$

And we know that $7.2$ is not an integer so it is not possible to have a regular polygon whose exterior angle is ${50}^o$