document.write( "Question 550746: Find the number of sides of a convex polygon if the measures of its interior angles have a sum of 6840° \n" ); document.write( "

Algebra.Com's Answer #359042 by KMST(5328) $\"\"$ $\"About$

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The sum of the measures of the interior angles of a convex polygon with n sides is (n-2)180°.
\n" ); document.write( "An easy way to understand and remember that is imagining a point in the interior of the polygon connected to all of the vertices forming n triangles.
\n" ); document.write( "The sum of all the angles in those triangles would be n(180°).
\n" ); document.write( "If you subtract the 2(180°)=360° corresponding to the angles at the point inside the polygon, you get the sum of the measures of the interior angles as (n-2)180°.
\n" ); document.write( "6840°/180°=38=n-2 --> n=40
\n" ); document.write( "The number of sides of that polygon is 40.
\n" ); document.write( "I am not going to draw it. \n" ); document.write( "

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