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Question Number 137732 by byaw last updated on 05/Apr/21
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.
$$\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{interior}\:\mathrm{angle} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{exterior}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{regular}\:\mathrm{polygon}\:\mathrm{is}\:\mathrm{5}:\mathrm{2}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{polygon}. \\ $$
Answered by mr W last updated on 05/Apr/21
interior angle + exterior angle =180°  interior angle / exterior angle =5/2  ⇒exterior angle =2/7×180°=((360°)/7)=((360°)/n)  ⇒n=7, i.e. the polygon has 7 sides.
$${interior}\:{angle}\:+\:{exterior}\:{angle}\:=\mathrm{180}° \\ $$$${interior}\:{angle}\:/\:{exterior}\:{angle}\:=\mathrm{5}/\mathrm{2} \\ $$$$\Rightarrow{exterior}\:{angle}\:=\mathrm{2}/\mathrm{7}×\mathrm{180}°=\frac{\mathrm{360}°}{\mathrm{7}}=\frac{\mathrm{360}°}{{n}} \\ $$$$\Rightarrow{n}=\mathrm{7},\:{i}.{e}.\:{the}\:{polygon}\:{has}\:\mathrm{7}\:{sides}. \\ $$
Commented by otchereabdullai@gmail.com last updated on 06/Apr/21
Thanks prof
$$\mathrm{Thanks}\:\mathrm{prof} \\ $$

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