Question

Is it possible to have a regular polygon each of whose interior angles is ${100}^0$?

Answer 1

For polygon of n sides,

Interior angle$=\frac{n-2}{n}\cdot {180}^{\circ }$

According to the question,

${100}^{\circ }=\frac{n-2}{n}\cdot {180}^{\circ }$

$\Rightarrow \frac{5}{9}=\frac{(n-2)}{\left(n\right)}$

$\Rightarrow 5n=9n-18$

$\Rightarrow 4n=18$

$\Rightarrow n=4.5$ which is not possible as n has to be a positive integer greater than or equal to 3.

$\therefore$ A regular polygon of interior angle ${100}^{\circ }$ is not possible.