Question

The interior angle of a regular polygon is ${156}^o$. Find the number of sides of the polygon.

Answer 1

Let the number of sides of the regular polygon be $n$.

So, Interior angle of the regular polygon $=\frac{[n-2]}{n}\times {180}^o$

Given, Interior angle $={156}^o$

So, $\frac{[n-2]}{n}\times {180}^o={156}^o$

$\Rightarrow 180n-360=156n$

$\Rightarrow 180n-156n=360$

$\Rightarrow 24n=360$

$\Rightarrow n=\frac{360}{24}$

$\Rightarrow n=15$

Therefore, the regular polygon with a interior angle of ${156}^o$ has $15$ sides.