If a polygon has 35 diagonals find the number of sides.

$$\begin{gathered} \mathrm{Let} \mathrm{no}. \mathrm{of} \mathrm{sides} \mathrm{of} \mathrm{a} \mathrm{polygon} = \mathrm{n} \\ \boxed{\mathrm{no}. \mathrm{of} \mathrm{diagonals} \mathrm{of} \mathrm{the} \mathrm{polygon}=\frac{\mathrm{n}\left(\mathrm{n}-3\right)}{2}} \\ \mathrm{given} \mathrm{that} \mathrm{no}. \mathrm{of} \mathrm{diagonals} =35 \\ \Rightarrow \frac{\mathrm{n}\left(\mathrm{n}-3\right)}{2}=35 \\ \Rightarrow \mathrm{n}\left(\mathrm{n}-3\right)=70 \\ \Rightarrow \mathrm{n}\left(\mathrm{n}-3\right)=10\left(7\right) \\ \Rightarrow \mathrm{n}=10 \end{gathered}$$