1.

The difference between the interior and exterior angles at a vertex of a regular polygon is 150°. The number of sides of the polygon is:1. 242. 103. 154. 30

Answer» Correct Answer - Option 1 : 24

Given:

The difference between the exterior and interior angles at a vertex of a regular polygon is 150°

Formula Used:

Interior angle of a polygon having side n = (n – 2)180°/n

Calculations:

Let Ai and Ae be interior and exterior angles

Sum of Ai and Ae = 180°,

So, Ai + Ae = 180

∴ Ai - Ae = 150

So, solving for Ae & Ai

Ae = 15°

Ai = 165°

Interior angle of a polygon having side n = (n – 2)180°/n

∴ 165° = (n – 2)180°/n

⇒ 165n = 180n – 360

⇒ 360 = 15n

⇒ n = 24

Thus number of sides is 24.


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