Question

If the difference between an exterior angle of a regular polygon of n sides and an exterior angle of another regular polygon of n+1 sides is equal to 5?; find the value of n

Answer 1

$$\begin{gathered} DearStudent \\ Theexteriorangleofansidedpolygon=\frac{{360}^0}{n} \\ Theexteriorangleofan+1sidedpolygon=\frac{{360}^0}{n+1} \\ given \\ \frac{360}{n}-\frac{360}{n+1}=5 \\ 360(\frac{n+1-n)}{n(n+1)}=5 \\ 360=5n(n+1) \\ 360=5n^2+5n \\ 5n^2+5n-360=0 \\ {n}^2+n-72=0 \\ {n}^2+9n-8n-72=0 \\ n(n+9)-8(n+9)=0 \\ (n-8\left)\right(n+9)=0 \\ n=8,-9 \\ ncannothavenegativevalue \\ thereforethevalueofn=8 \end{gathered}$$