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

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

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

$$interiorangle+exteriorangle=180°$$$$interiorangle/exteriorangle=5/2$$$$\Rightarrow exteriorangle=2/7\times 180°=\frac{360°}{7}=\frac{360°}{n}$$$$\Rightarrow n=7,i.e.thepolygonhas7sides.$$

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

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

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