document.write( "Question 471072: how many diagonals does a polygon have if its angle sum is 1080 degrees ? \n" ); document.write( "

Algebra.Com's Answer #323121 by ccs2011(207) $\"\"$ $\"About$

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First find the number of sides of the polygon:
\n" ); document.write( " $\"180%28n-2%29+=+1080\"$
\n" ); document.write( " $\"n-2+=+6\"$
\n" ); document.write( " $\"n+=+8\"$
\n" ); document.write( "Next find the number of diagonals in a octagon:
\n" ); document.write( "There are 8 vertices and from each vertex 5 diagonals can be drawn.
\n" ); document.write( "**you can't draw a diagonal to an adjacent vertex or to itself**
\n" ); document.write( "Also each diagonal is shared by 2 vertices
\n" ); document.write( "This leads to the general formula: $\"%28n%28n-3%29%29%2F2\"$
\n" ); document.write( "diagonals = $\"%288%29%285%29%2F2+=+20\"$ \n" ); document.write( "

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