A polygon has 35 diagonals. How many sides does it have?

[tex]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

[/tex]