Question

Is it possible to have a regular polygon if each interior angle is $125°$

Answer 1

Each interior angle of polygon of sides $n$ is $\frac{\left(n-2\right)\times 180°}{n}$

$$\begin{gathered} \Rightarrow \frac{\left(n-2\right)\times 180°}{n}=125° \\ \Rightarrow 180n-360=125n \\ \Rightarrow 55n=360 \\ \Rightarrow n=\frac{360}{55}=6.545 \end{gathered}$$

Since, $n$ denotes number of sides of polygon, it cannot be $6.545.$

Hence, it not possible to have a regular polygon if each interior angle is $125°$