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If the sum of the interior angles of a polygon equals 100...
by diana
if the sum of the interior angles of a polygon equals 100 straight angles, how many sides does the polygon have?
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You know that the sum of the interior angles of a simple n-gon polygon is (n - 2) p radians or (180n -360) degrees. The logic for it is because any simple n-gon can be considered to be made up of (n - 2) triangles, each of which has an angle sum of 180 degrees or p radians.
In the question the sum of the interior angles of a polygon equals 100 straight angles i.e. 100* 180 degrees (as straight angle equals 180 deg). It equals to 1800 degrees.
Thus (180n -360) = 18000. Simplify it and find value of n.
180n =18360, which gives n = 102 sides.

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by Winpossible
May 01, 10 08:58AM PST
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