Question

Find the number of sides of a regular polygon if each of its interior angles measure $120°$.

Answer 1

Find the number of sides of regular of polygon.

It is given that the Interior angle of the polygon is $120°$.

We have to find the number of sides of a regular polygon.

Suppose $\mathrm{n}$ is the number of sides of the regular polygon.

For a regular polygon, the size of each interior angle is,

One angle measure $=\frac{180°\times \left(\mathrm{n}-2\right)}{\mathrm{n}}$

Substitute the given value in the above formula, we get,

$\therefore \frac{180°\times \left(\mathrm{n}-2\right)}{\mathrm{n}}=120°$

$\Rightarrow$ $180\mathrm{n}-360=120\mathrm{n}$

$\Rightarrow$ $60\mathrm{n}=360$

$\Rightarrow$ $\mathrm{n}=6$

Hence, the regular polygon has $6$ sides.