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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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