Question Number 175893 by blackmamba last updated on 08/Sep/22
$$\:{If}\:{outer}\:{angle}\:{in}\:{n}−{polygone}\:{is}\:\mathrm{18}° \\ $$$$\:{find}\:{n} \\ $$
Commented by Rasheed.Sindhi last updated on 09/Sep/22
$${n}=\mathrm{20} \\ $$
Commented by blackmamba last updated on 09/Sep/22
$${what}\:{the}\:{formula} \\ $$
Commented by BaliramKumar last updated on 09/Sep/22
$$\frac{\mathrm{360}}{\mathrm{18}}\:=\:\mathrm{20} \\ $$
Answered by Rasheed.Sindhi last updated on 09/Sep/22
$${Central}\:{angle}:\:\mathrm{360}/{n} \\ $$$${Angle}\:{between}\:{consecutive}\:{sides}: \\ $$$$\mathrm{180}−\frac{\mathrm{360}}{{n}}=\frac{\mathrm{180}{n}−\mathrm{360}}{{n}} \\ $$$${outer}\:\:{angle}:\:\:\mathrm{180}−\frac{\mathrm{180}{n}−\mathrm{360}}{{n}} \\ $$$$\:\:=\frac{\mathrm{180}{n}−\mathrm{180}{n}+\mathrm{360}}{{n}}=\frac{\mathrm{360}}{{n}} \\ $$$$\frac{\mathrm{360}}{{n}}=\mathrm{18}\Rightarrow{n}=\frac{\mathrm{360}}{\mathrm{18}}=\mathrm{20} \\ $$$$\begin{array}{|c|}{\underset{\overset{} {\mathrm{n}=\frac{\mathrm{360}}{\mathrm{Outer}\:\mathrm{angle}}}} {\mathrm{Outer}\:\mathrm{angle}=\frac{\mathrm{360}}{\mathrm{n}}}}\\\hline\end{array} \\ $$
Commented by peter frank last updated on 09/Sep/22
$$\mathrm{thanks} \\ $$
Commented by Tawa11 last updated on 15/Sep/22
$$\mathrm{Great}\:\mathrm{sir}. \\ $$