1.

How many diagonals can an n-gon (a polygon with n sides ) have ?

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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