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

  • question_answer
    External angle of a regular polygon is \[72{}^\circ .\]Find the sum of all the internal angles of it.

    A) \[360{}^\circ \]

    B) \[480{}^\circ \]

    C) \[352{}^\circ \]

    D) \[540{}^\circ \]

    Correct Answer: D

    Solution :

    [d] External angle of any polygon \[72{}^\circ =\frac{260{}^\circ }{n}\]\[\Rightarrow \]\[n=5\] \[\therefore \]Given, polygon is regular pentagon. \[\therefore \]Every interior angle of it \[=180{}^\circ -\] External angle \[=180{}^\circ -72{}^\circ =108{}^\circ \] \[\therefore \]Sum of total interior angles of it \[=5\times 108{}^\circ =540{}^\circ \]


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