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The degree measure of the sum of the interior angles of a convex polygon with n sides is 1800. What is the degree measure of the sum of the interior angles of a convex polygon with n + 2 sides?

 May 16, 2020
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If the sum of the interior angles of a polygon with n sides is x degrees, then the sum of the interior angles of a polygon with n+1 sides is x+180 degrees and a polygon with n+2 sides is x+360 degrees. A quick proof for this is that you can draw n-2 triangles in an n-gon such that each triangle's three vertices are vertices of the polgon. In a n+1-gon there is one more triangle contributing 180 more degrees. So 1800+360 is 2160.

 May 16, 2020

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