SOLUTION: Is it possible to have a polygon whose sum of the interior angles is 500?

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Question 595652: Is it possible to have a polygon whose sum of the interior angles is 500?
Answer by math-vortex(648) About Me  (Show Source):
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Is it possible to have a polygon whose sum of the interior angles is 500?
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Hi, there--
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Let's have S be the sum of the interior angles in a polygon, and have n be the number of sides in the polygon. The formula for finding the sum of the interior angles of any polygon is
S=%28180%29%28n-2%29
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[NOTE: Here is a website with an animated graphic that you can experiment with to see how this works. http://www.mathopenref.com/polygoninteriorangles.html]
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You want a polygon with an interior angle sum of 500. Let's set S equal to 500 and see what how many sides such a polygon would have.
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S=180%28n-2%29
500=180%28n-2%29
500=180n-360
860=180n
n=860%2F180
n=43%2F9
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We cannot have a polygon with 43/9 sides, so we know that an interior angle sum of 500 is impossible.
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Hope this helps! Feel free to email me if some part of this explanation is unclear.
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Ms.Figgy
math.in.the.vortex@mail.com