A polygon has 54 diagonals. Then,the number o | vedclass

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(D) The number of diagonals in a polygon with $n$ sides is given by the formula $\frac{n(n-3)}{2}$.Given that the number of diagonals is $54$,we have:

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$12$

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(D) The number of diagonals in a polygon with $n$ sides is given by the formula $\frac{n(n-3)}{2}$.Given that the number of diagonals is $54$,we have:$\frac{n(n-3)}{2} = 54$$n(n-3) = 108$$n^2 - 3n - 108 = 0$Factoring the quadratic equation:$n^2 - 12n + 9n - 108 = 0$$n(n - 12) + 9(n - 12) = 0$$(n + 9)(n - 12) = 0$Since the number of sides $n$ must be positive,we have $n = 12$.Therefore,the number of sides in the polygon is $12$.

$A$ polygon has $54$ diagonals. Then,the number of its sides is

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