Question:
Is it possible to have a regular polygon each of whose exterior angles is 50°?
Solution:
Each exterior angle of an $n$-sided polygon $=\left(\frac{360}{n}\right)^{\circ}$
If the exterior angle is $50^{\circ}$, then:
$\frac{360}{n}=50$
$\Rightarrow n=7.2$
Since n is not an integer, we cannot have a polygon with each exterior angle equal to 50°.