Question

Is it possible to have a regular polygon whose each interior angle is $130°$?

Answer 1

Each interior angle of a regular polygon is given by $\frac{(n-2)\times 180°}{n}$where $n$ is the number of sides of that polygon.

So, $$\begin{gathered} \frac{(n-2)\times 180°}{n}=130° \\ 180n-360=130n \\ 50n=360 \\ n=7.2 \end{gathered}$$

The number of sides of a polygon has to be a natural number.

Since, $n$ is the number of the sides of a polygon, it cannot have the value of $7.2$

Hence, it is not possible to have a regular polygon whose each interior angle is $130°$