If each interior angle of a regular polygon is 120°, then find the number of diagonals of the polygon.

Correct option is A

Given:

Each interior angle of a regular polygon is 120°.

Concept Used:

Interior angle of a regular polygon = (n - 2) $$\times\frac{ 180° }{ n}$$​, where 'n' is the number of sides.

Number of diagonals in a polygon = $$\frac{n(n - 3) } 2$$​​

Solution:

120° = (n - 2) $$\times\frac{ 180° }{ n}$$​​

120n = 180n - 360

60n = 360

n = 6

Number of diagonals =$$\frac{6(6 - 3) } 2$$​​

Number of diagonals = 9