Question

The interior angle of a regular polygon is ${140}^{\circ }$. Find the number of sides of that polygon.

Answer 1

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

Since the interior angle of the given regular polygon is ${140}^{\circ }$.

The sum of the interior angles $=(2n-4)\times$ right angles.

So, $140n=(2n-4)\times {90}^{\circ }$

or, $140n=180n-360$

or, $40n=360$

or, $n=9$ sides.
Hence, the number of sides in the given polygon is $9$.