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Question Number 175893 by blackmamba last updated on 08/Sep/22

If outer angle in n−polygone is 18° find n

$$\:{If}\:{outer}\:{angle}\:{in}\:{n}−{polygone}\:{is}\:\mathrm{18}° \\ $$$$\:{find}\:{n} \\ $$

Commented by Rasheed.Sindhi last updated on 09/Sep/22

n=20

$${n}=\mathrm{20} \\ $$

Commented by blackmamba last updated on 09/Sep/22

what the formula

$${what}\:{the}\:{formula} \\ $$

Commented by BaliramKumar last updated on 09/Sep/22

((360)/(18)) = 20

$$\frac{\mathrm{360}}{\mathrm{18}}\:=\:\mathrm{20} \\ $$

Answered by Rasheed.Sindhi last updated on 09/Sep/22

Central angle: 360/n Angle between consecutive sides: 180−((360)/n)=((180n−360)/n) outer angle: 180−((180n−360)/n) =((180n−180n+360)/n)=((360)/n) ((360)/n)=18⇒n=((360)/(18))=20 determinant (((Outer angle=((360)/n)_(n=((360)/(Outer angle))^() ) )))

$${Central}\:{angle}:\:\mathrm{360}/{n} \\ $$$${Angle}\:{between}\:{consecutive}\:{sides}: \\ $$$$\mathrm{180}−\frac{\mathrm{360}}{{n}}=\frac{\mathrm{180}{n}−\mathrm{360}}{{n}} \\ $$$${outer}\:\:{angle}:\:\:\mathrm{180}−\frac{\mathrm{180}{n}−\mathrm{360}}{{n}} \\ $$$$\:\:=\frac{\mathrm{180}{n}−\mathrm{180}{n}+\mathrm{360}}{{n}}=\frac{\mathrm{360}}{{n}} \\ $$$$\frac{\mathrm{360}}{{n}}=\mathrm{18}\Rightarrow{n}=\frac{\mathrm{360}}{\mathrm{18}}=\mathrm{20} \\ $$$$\begin{array}{|c|}{\underset{\overset{} {\mathrm{n}=\frac{\mathrm{360}}{\mathrm{Outer}\:\mathrm{angle}}}} {\mathrm{Outer}\:\mathrm{angle}=\frac{\mathrm{360}}{\mathrm{n}}}}\\\hline\end{array} \\ $$

Commented by peter frank last updated on 09/Sep/22

thanks

$$\mathrm{thanks} \\ $$

Commented by Tawa11 last updated on 15/Sep/22

Great sir.

$$\mathrm{Great}\:\mathrm{sir}. \\ $$

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