The interior angles of which of the following regular polygons is 140° each ?

Question

Question

This question was previously asked in

OSSSC GPEO Prelims GS Official Paper 2015 (Held on: 13th Dec 2015)

Answer 1

Given data:

1. Each interior angle of the regular polygon is 140°.

Formula used:

The formula for the interior angle of a regular polygon is given by (n-2)×180°/n, where n is the number of sides of the polygon.

Solution:

1. We need to find the value of n for which the interior angle is 140°. So, we set up the equation (n-2)×180°/n = 140°.

⇒ n - 2 = 140n/180

⇒ 180n - 360 = 140n

⇒ 40n = 360

⇒ n = 360/40

⇒ n = 9

Therefore, the regular polygon with each interior angle of 140° is a nonagon.