If a polygon of n sides has 560 diagonals,the | vedclass

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(A) The number of line segments obtained by joining $n$ vertices of an $n$-sided polygon is given by ${}^nC_2$.Out of these segments,$n$ segments are

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$35$

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(A) The number of line segments obtained by joining $n$ vertices of an $n$-sided polygon is given by ${}^nC_2$.Out of these segments,$n$ segments are the sides of the polygon.Therefore,the number of diagonals is ${}^nC_2 - n$.Given that the number of diagonals is $560$,we have:${}^nC_2 - n = 560$$\Rightarrow \frac{n(n-1)}{2} - n = 560$$\Rightarrow n^2 - n - 2n = 1120$$\Rightarrow n^2 - 3n - 1120 = 0$Solving the quadratic equation:$(n - 35)(n + 32) = 0$Since $n$ must be a positive integer,$n = 35$.

If a polygon of $n$ sides has $560$ diagonals,then $n=$

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