the-ratio-of-the-interior-angle-to-the-exterior-angle-of-a-regular-polygon-is-5-2-Find-the-number-of-sides-of-the-polygon-

Question Number 137732 by byaw last updated on 05/Apr/21

$$\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{interior}\:\mathrm{angle} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{exterior}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{regular}\:\mathrm{polygon}\:\mathrm{is}\:\mathrm{5}:\mathrm{2}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{polygon}. \\ $$

Answered by mr W last updated on 05/Apr/21

$${interior}\:{angle}\:+\:{exterior}\:{angle}\:=\mathrm{180}° \\ $$$${interior}\:{angle}\:/\:{exterior}\:{angle}\:=\mathrm{5}/\mathrm{2} \\ $$$$\Rightarrow{exterior}\:{angle}\:=\mathrm{2}/\mathrm{7}×\mathrm{180}°=\frac{\mathrm{360}°}{\mathrm{7}}=\frac{\mathrm{360}°}{{n}} \\ $$$$\Rightarrow{n}=\mathrm{7},\:{i}.{e}.\:{the}\:{polygon}\:{has}\:\mathrm{7}\:{sides}. \\ $$

Commented by otchereabdullai@gmail.com last updated on 06/Apr/21

$$\mathrm{Thanks}\:\mathrm{prof} \\ $$

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