document.write( "Question 809163: Can someone explain why the formula (n - 2)180 can be used to find the sum of the interior angles of a polygon? \n" ); document.write( "

Algebra.Com's Answer #487451 by rothauserc(4718) $\"\"$ $\"About$

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we know the sum of the interior angles of a triangle is 180 degrees,
\n" ); document.write( "consider triangle ABC with a line parallel to the base (AB) and touching angle C, then AC and BC are transversals and angles A+B+C = 180 degrees. We see this because alternate interior angles are equal on a transversal and angles A+B+C do a complete rotation from one side of the straight line to the other or 180 degrees.
\n" ); document.write( "Now consider the pentagon ABCDE,
\n" ); document.write( "Start with vertex A and connect it to all other vertices (it is already connected to B and E by the sides of the pentagon). Three triangles are formed. The sum of the angles in each triangle contains 180 degrees. The total number of degrees in all three triangles will be 3 times 180 or 540 degrees.
\n" ); document.write( "Note that the Pentagon has 5 sides and 3 triangles were formed by connecting the vertices. The number of triangles formed by connecting the vertices of a polygon will always be 2 less than the number of sides, n. Therefore we have,
\n" ); document.write( "sum of interior angles of a polygon is (n-2)*180 where n is the number of sides.
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