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

  • question_answer
    If difference between exterior and interior angles of a polygon is \[60{}^\circ ,\]then find the number of sides in the polygon.

    A) 4

    B) 5

    C) 6

    D) 7

    Correct Answer: C

    Solution :

    [c] Exterior angle \[-\] Interior angle \[=60{}^\circ \] \[\Rightarrow \]   \[\frac{(n-2)\times 180{}^\circ }{n}-\frac{360{}^\circ }{n}=60{}^\circ \] \[\Rightarrow \]   \[\frac{1}{n}[(n-2)\times 180{}^\circ -360{}^\circ ]=60{}^\circ \] \[\Rightarrow \]   \[\frac{1}{n}[180{}^\circ n-360{}^\circ -360{}^\circ ]=60{}^\circ \] \[\Rightarrow \]   \[180{}^\circ n-720{}^\circ =60{}^\circ n\] \[\Rightarrow \]   \[120{}^\circ n=720{}^\circ \] \[\Rightarrow \]   \[n=\frac{720{}^\circ }{120{}^\circ }=6\]


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