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Math Help - Equation needed - Regular polygon question!

  1. #1
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    Equation needed - Regular polygon question!

    Question:
    Each exterior angle of a regular polygon of n sides exceeds by 6deg each exterior ngle of a regular polygon of 2n sides. Find an equation for n and solve it.

    I believe it involves some of the facts like:
    * All sides and angles of a regular polygon are equal.
    * The sum of exterior angles equals to 360deg.
    * Each interior + exterior angle equals to 180deg.

    But I am still not sure how to construct an equation for this problem. I guess I am just weak at constructing simultaneous or similar linear equations.
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  2. #2
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    Hello, struck!

    You have all the necessary information ... just put it together.


    Each exterior angle of a regular polygon of n sides
    exceeds by 6 each exterior angle of a regular polygon of 2n sides.
    Find an equation for n and solve it.

    I believe it involves some of the facts like:
    . . All sides and angles of a regular polygon are equal.
    . . The sum of exterior angles equals to 360.
    . . Each interior + exterior angle equals 180.

    The sum of the exterior angles is always 360.

    In a regular polygon of n sides, each exterior angle has \frac{360}{n} degrees. .[1]

    In a regular polygon of 2n sides, each exterior angle has \frac{360}{2n} degrees. .[2]


    We are told that [1] is 6 greater than [2].

    Hence: . \boxed{\frac{360}{n} \:=\:\frac{180}{n} + 6}

    Multiply by n\!:\;\;360 \:=\:180 + 6n\quad\Rightarrow\quad\boxed{n\:=\:30}


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