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Math Help - angles of polygon

  1. #1
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    angles of polygon

    Find the number of sides of a regular polygon in which the interior angle is four times the exterior angle
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  2. #2
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    Quote Originally Posted by helkp View Post
    Find the number of sides of a regular polygon in which the interior angle is four times the exterior angle
    The sum of the angles a regular polygon is
    180(n-2)
    And there are n angles as well as sides.
    Thus, each angle has,
    Code:
    180(n-2)
    ----------
         n
    Degree.

    The sum of all exterior angles is always 360 degree.
    Divided by the number of angles n thus each one has,
    Code:
       360
       ----
         n
    By the conditions of the problem you are trying to solve,
    Code:
    180(n-2)       4*360
    ------------  = ----
           n              n
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  3. #3
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    Hello, helkp!

    It would help if you knew some formulas.
    If you don't, you could wait for years for Divine Inspiration . . .


    Find the number of sides of a regular polygon in which the interior angle
    is four times the exterior angle

    A regular polygon of n sides has a total of 180(n - 2) degrees in its interior.
    So each interior angle has: 180(n - 2)/n degrees.

    An exterior angle is the supplement of an interior angle.
    Hence, an exterior angle has: . 180 - 180(n - 2)/2 = 360/n degrees.


    We are told that: .[Interior angle] .= .4 [Exterior angle]

    . . . .So we have: . 180(n - 2)/n . = .4 . (360/n)


    Can you finish it now?

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