A regular polygon of n sides has 170 diagonals. Then n =

No of sides of regular polygon = n

No of diagonals $=\frac{\mathrm{n}(\mathrm{n}-3)}{2}=170$

$$\begin{gathered} \mathrm{n}(\mathrm{n}-3)=17\times 10\times 2 \\ \Rightarrow \mathrm{n}(\mathrm{n}-3)=20\times 17 \Rightarrow \boxed{\mathrm{n}=20} \end{gathered}$$