Question

How many sides does a regular polygon has if each of it's interior angle is ${120}^{\circ }$?

Answer 1

Let assume polygon is regular polygon.

The measure of an interior angle, $A$, of a regular polygon of $n$ sides is given by:

$A=\frac{(n-2){180}^o}{n}$

$\Rightarrow$ ${120}^o=\frac{(n-2)}{n}\times {180}^o.$

$\Rightarrow$ $\frac{{120}^{o}n}{{180}^o}=n-2$

$\Rightarrow$ $\frac{2}{3}n=n-2$

$\Rightarrow$ $2n=3n-6$

$\Rightarrow$ $n=6$

$\therefore$ The regular polygon has $6$ equal sides and is called a $hexagon.$