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Math Help - Sequence & Series problem

  1. #1
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    Sequence & Series problem

    The smallest angle of a polygon is 120 degree. It increases by 5 degree with every angle. Find the number of sides(n).

    I did this using

    180(n-2)=120+125+130+......n terms
    I solved this and found two answers: 9 and 16.

    But the answer is given only 9. My friend said that the other answer was related to sum of exterior angles...

    Thanks.
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  2. #2
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    Re: Sequence & Series problem

    If you try to have 16 sides with your smallest interior angle being 120, your exterior angles start going negative. This is easy to see as the exterior angle is 180-(interior angle). Interior angles are 120,125...120+5(n-1). at n=13 the largest interior angle tries to be 180 deg and you no longer have a polygon.

    Having only 9 sides satisfies your conditions above and remains a polygon.
    Thanks from AaPa
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  3. #3
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    Re: Sequence & Series problem

    thanks.
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