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The difference between the interior and exterior angles of a regular polygon is 60°. Find the number of sides in the polygon.
Question

The difference between the interior and exterior angles of a regular polygon is 60°. Find the number of sides in the polygon.

A.

4

B.

5

C.

6

D.

7

Correct option is C

Let the number of sides be n.n.​ 
Exterior angle of a regular polygon  =360n \frac{360^\circ}{n} \\​​
Interior angle = 180360n 180^\circ - \frac{360^\circ}{n} \\​​
Given: Interior angle - Exterior angle = 6060^\circ \\​​
=>(180360n)360n=60=>180720n=60=>720n=120=>n=720120=6\Rightarrow \left(180^\circ - \frac{360^\circ}{n}\right) - \frac{360^\circ}{n} = 60^\circ \\\Rightarrow 180^\circ - \frac{720^\circ}{n} = 60^\circ \\\Rightarrow \frac{720^\circ}{n} = 120^\circ \\\Rightarrow n = \frac{720^\circ}{120^\circ} = 6​​
Correct answer is (c) 6

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