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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2006

  • question_answer
    The interior angles of a polygon are in AP. The smallest angle is\[120{}^\circ \]and the common difference is\[5{}^\circ \]. The number of sides of the polygon is:

    A)  9                            

    B)         10

    C)  16                         

    D)         5

    E)  8

    Correct Answer: A

    Solution :

    Let there be n sides of the polygon. Then, the sum of all interior angles is\[(2n-4)\]right angles. \[\therefore \]  \[\frac{n}{2}[240+(n-1)5]=(2n-4)\times 90\] \[\Rightarrow \]               \[{{n}^{2}}-25n+144=0\] \[\Rightarrow \]               \[n=9,16\] But for\[n=16,\]the largest angle is \[120+(16-1)5=195,\]which is impossible Hence,\[n=9\].


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