document.write( "Question 226229: If a polygon has 42 sides, how many diagonals does it have?
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Algebra.Com's Answer #168521 by Edwin McCravy(20056) $\"\"$ $\"About$

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If a polygon has 42 sides, how many diagonals does it have?
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document.write( "If you connect any vertex to any other vertex besides the 2\r\n" );
document.write( "next to it, you will get a diagonal.\r\n" );
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document.write( "Every vertex is a connected pair of vertices. However, not \r\n" );
document.write( "every connected pair of vertices are diagonals.\r\n" );
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document.write( "But first we calculate the number of all pairs of vertices.\r\n" );
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document.write( "That's 42C2.\r\n" );
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document.write( "However, this is too many because each side is also\r\n" );
document.write( "a connected pair of vertices.  \r\n" );
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document.write( "(Note: If you connect a vertex to either of the two\r\n" );
document.write( "vertices on each side of it, you will NOT get\r\n" );
document.write( "a diagonal, but you will only retrace two sides of \r\n" );
document.write( "the polygon.) \r\n" );
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document.write( "So we must subtract the 42 sides from the total number\r\n" );
document.write( "of vertex pairs, for the 42C2 counts them, too. \r\n" );
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document.write( "Answer: \r\n" );
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document.write( "Edwin

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