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Math Help - Number of sides of a polygon

  1. #1
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    Number of sides of a polygon



    A, B and C are three vertices of a polygon as shown above. The reflex angle ABC = 222^o and the size of the remaining exterior angles are equal to 53^o each. Calculate the number of sides this polygon has.
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  2. #2
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    Quote Originally Posted by Punch View Post
    A, B and C are three vertices of a polygon as shown above. The reflex angle ABC = 222^o and the size of the remaining exterior angles are equal to 53^o each. Calculate the number of sides this polygon has.
    Sum of measures of exterior angles of a (simple) polygon is 360 degrees. So...
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  3. #3
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    note that not all the exterior angles are equal...


    360-222=138

    360/53 will not work
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    To calculate the total angle of all the interior angles added, we use:

    a=180(n-2)

    a = sum of total internal angles
    n = number of sides

    Now given the information:
    - One internal angle is 138 degrees
    - The rest of the internal angles are 127 degrees

    Therefore, the total internal angle can be calculated by:

    a = 127(n-1) + 138

    Now use simultaneous equation to solve for n.
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  5. #5
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    Quote Originally Posted by Punch View Post
    note that not all the exterior angles are equal...
    Yes I know.

    Quote Originally Posted by Punch View Post
    360-222=138
    No, exterior angle is 222-180 = 42

    Quote Originally Posted by Punch View Post
    360/53 will not work
    And that's not what I was suggesting.

    42 + (n-1)53 = 360. Solve for n.
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  6. #6
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    Accidental double post. (I pressed submit once, and then it told me it didn't post because I had to wait 30 seconds between posts, but actually it had posted...)
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