find the no of sides of a polygon the sum of whose interior angles is 1620

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{Let} \mathrm{n} \mathrm{be} \mathrm{number} \mathrm{of} \mathrm{sides}: \\ \Rightarrow \left(\mathrm{n}-2\right)\times 180°=\mathrm{Sum} \mathrm{of} \mathrm{all} \mathrm{interior} \mathrm{angles} \\ \Rightarrow \left(\mathrm{n}-2\right)\times 180°=1620° \\ \Rightarrow \mathrm{n}-2=\frac{1620°}{180°}=9 \\ \Rightarrow \mathrm{n}=9+2 \\ \Rightarrow \mathrm{n}=11 \left(\mathrm{Answer}\right) \end{gathered}$$
​

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.
Regards