Question

The measure of interior angle of a regular polygon is 120°. Find the number of sides the polygon has.​

Answer 1

Given-

The measure of interior angle of a regular polygon = 120°

To Find-

Number of sides the polygon

Solution-

Sum of interior angles of a regular polygon

= (n − 2) × 180°

Interior angle of a regular polygon

= $\large\frac{[(n − 2) × 180°]}{n}$

$\implies$120n = [(n − 2) × 180°]

$\implies$120n = 180n - 360

$\implies$60n = 360

$\boxed{\sf\:n=6}$

Therefore,polygon has 6 sides and it is hexagon.