Question

Is it possible to have a regular polygon each of whose interior angles is ${100}^{\circ }$?

Answer 1

Let interior angle of a polygon having n sides = ${100}^{\circ }$ $\therefore$ $\frac{2n-4}{n}\times {90}^{\circ }={100}^{\circ }$ $\Rightarrow$ $\frac{2n-4}{n}$=$\frac{100}{90}$=$\frac{10}{9}$ $\Rightarrow$ 18n-36 = 10n $\Rightarrow$ 18n-10n = 36 8n = 36$\Rightarrow$n = $\frac{36}{8}$=$\frac{9}{2}$ Which is not a whole number $\therefore$ It is not possible