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One way to think of this is to join all the vertices of the polygon to a single point call this point X. For a n-sided poygon, you now have n triangles. The sum of all the angles of each triangle is 180 degrees. So all the angles of all the n triangles add to n*180 degrees.
But, this sum includes all the angles around the point X and these add to 360 = 2*180 degrees. These need to be taken away. So (n-2)*180 degrees.
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