document.write( "Question 560250: is it possible to have a polygon whose sum of interior angle is
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document.write( "(1) 7 right angle
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document.write( "(2) 4500 \n" );
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Algebra.Com's Answer #363837 by Theo(13342)![]() ![]() You can put this solution on YOUR website! the formula for the sum of the interior angles of a polygon is: \n" ); document.write( "S = 180 * (n-2) \n" ); document.write( "if n = 3 (triangle), then S = 180 * (3-2) = 180 \n" ); document.write( "if n = 4 (quadrilateral), then S = 180 * (4-2) = 360 \n" ); document.write( "from the formula for S, we can derive the formula for n as follows: \n" ); document.write( "S = 180 * (n-2) \n" ); document.write( "divide both sides of this equation by 180 to get: \n" ); document.write( "S / 180 = n-2 \n" ); document.write( "add 2 to both sides of this equation to get: \n" ); document.write( "n = (S/180) + 2 \n" ); document.write( "for the triangle, we get: \n" ); document.write( "n = (180/180) + 2 which equals 1 + 2 which equals 3. \n" ); document.write( "for the quadrilateral, we get: \n" ); document.write( "n = (360/180) + 2 which equals 2 + 2 which equals 4. \n" ); document.write( "if the sum of the interior angles is 4500, then the formula becoms: \n" ); document.write( "n = (4500/180) + 2 which becomes: \n" ); document.write( "n = 25 + 2 which becomes: \n" ); document.write( "n = 27 \n" ); document.write( "i'm not sure what you mean by 7 right angle. \n" ); document.write( "if you mean 7 * a right angle, then the sum would be 7 * 90 = 630 degrees. \n" ); document.write( "the formula becomes: \n" ); document.write( "n = (630/180) + 2 which becomes: \n" ); document.write( "n = 3.5 + 2 which becomes: \n" ); document.write( "n = 5.5 \n" ); document.write( "since n has to be an integer, the sum of angles equal to 630 degrees would not be possible. \n" ); document.write( "if n is 5, the sum is 3 * 180 = 540 degrees. \n" ); document.write( "if n is 6, the sum is 4 * 180 = 720 degrees. \n" ); document.write( " \n" ); document.write( " |