document.write( "Question 50726: How many diagonal lines are in a dodecagon?\r
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document.write( "How many diagonal lines are in a hexadegon?
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Algebra.Com's Answer #33787 by AnlytcPhil(1806)![]() ![]() You can put this solution on YOUR website! How many diagonal lines are in a dodecagon? \r\n" ); document.write( "\r\n" ); document.write( "A dodecagon has 12 sides and 12 vertices. Every combination of two vertices,\r\n" ); document.write( "except the combinations representing the 12 sides, will represent a diagonal\r\n" ); document.write( "line. Therefore\r\n" ); document.write( "\r\n" ); document.write( "C(12,2) - 12 = 12!/[2!(12-2)!] - 12 = 12!/(2!10!) - 12 = 66 - 12 = 54\r\n" ); document.write( "\r\n" ); document.write( "How many diagonal lines are in a hexadecagon?\r\n" ); document.write( "\r\n" ); document.write( "A hexadecagon has 16 sides and 16 vertices. Every combination of two vertices,\r\n" ); document.write( "except the conbinations representing the 16 sides, will represent a diagonal\r\n" ); document.write( "line. Therefore\r\n" ); document.write( "\r\n" ); document.write( "C(16,2) - 16 = 16!/[2!(16-2)!] - 16 = 16!/(2!14!) - 16 = 120 - 16 = 104\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |