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Question 17947: What is the polygon exterior angle sum theorem?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! take any regular polygon of n sides(call it ABCDE....etc...) .let its centre be P.join P to each vertex A,B,C,D,E...etc..we get n triangles namely PAB,PBC,PCD,PDE...etc..sum of all angles in all those n triangles =n*sum of angles in one triangle =180*n...this sum includes sum of all interior angles in the polygon + angles all around P which as we know is 360.hence sum of all interior angles=n*180-360=90*(2n-4)degrees...hence
sum of all interior angles of a regular polygon =(2n-4)*90 degrees
each interior angle incase of a regular polygon =(2n-4)*90/n=say x....if exterior angle is y
, we have x+y=180..
hence y=180-x=180-[(2n-4)*90/n]=exterior angle of a regular polygon
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