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SSC Quantitative Aptitude Quadratic Equations Question Bank Quadrilateral and Polygon (I)

  • question_answer
    The difference between the interior and exterior angles of a regular polygon is \[60{}^\circ .\]Then, how many sides are there in that polygon?

    A) 5

    B) 6

    C) 7

    D) 8

    Correct Answer: B

    Solution :

    [b] Here, (interior angle) - (exterior angle) \[=60{}^\circ \] \[\Rightarrow \]   \[\frac{(n-2)\times 180{}^\circ }{n}-\frac{360{}^\circ }{n}=60{}^\circ \] \[\Rightarrow \]   \[\frac{1}{n}[(n-2)\times 180{}^\circ -360{}^\circ ]=60{}^\circ \] \[\Rightarrow \]   \[\frac{1}{n}[180{}^\circ n-360{}^\circ -360{}^\circ ]=60{}^\circ \] \[\Rightarrow \]   \[180{}^\circ n-60{}^\circ n=720{}^\circ \] \[80{}^\circ n-60{}^\circ n=720{}^\circ \] \[120{}^\circ n=720{}^\circ \] \[n=6\] Therefore, the polygon contains 6 sides and it is called hexagon.


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