(C) 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 $35$,we have:

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(C) 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 $35$,we have:$\frac{n(n-3)}{2} = 35$$n(n-3) = 70$$n^2 - 3n - 70 = 0$Factoring the quadratic equation:$(n - 10)(n + 7) = 0$Since $n$ must be a positive integer,we have $n = 10$.Therefore,the number of sides is $10$.

Class 11 Mathematics Permutation and Combination Geometrical problems

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$A$ polygon has $35$ diagonals,then the number of its sides is

A
$8$
B
$9$
C
$10$
D
$11$

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$A$ polygon has $35$ diagonals,then the number of its sides is

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