[d=35\ d=\frac{n(n-3)}{2}\ d=\frac{n(n-3)}{2}\35=\frac{n(n-3)}{2}\ 70=n^2-3n\ n^2-3n-70=0\ n^2-10n+7n-70=0\ n(n-10)+7(n-10)=0\ (n+7)(n-10)=0\ n=-7 \vee n=10\\ n=10
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A polygon with 35 diagonals has 10 sides, making it a decagon. This is found using the formula for the number of diagonals in a polygon. By solving the quadratic equation derived from this formula, we determine that the only feasible solution is 10 sides.
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