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How many diagonals can an n-gon (a polygon with n sides ) have ? |
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Answer» Solution :"A POLYGON of N-sides has n vertices". `:.` "The NUMBER of ST. LINES joining the n-vertices is" `""^nC_2`. `:.` "The number of diagonals is" `""^nC_2-n` `= (n!)/(2!(n-4)!)-n=(n(n-1))/2-n` `= (n^2-n-2n)/2=(n^2-3n)/2=(n(n-3))/2` |
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