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Question Number 142282 by pete last updated on 29/May/21

$$\mathrm{Three}\mathrm{interior}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{polygon}\mathrm{are}160°$$$$\mathrm{each}.\mathrm{If}\mathrm{the}\mathrm{other}\mathrm{interior}\mathrm{angles}\mathrm{are}120°\mathrm{each},$$$$\mathrm{find}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{sides}\mathrm{of}\mathrm{the}\mathrm{polygon}.$$

Answered by som(math1967) last updated on 29/May/21

$$\mathit{l}\mathit{e}\mathit{t}\mathit{n}\mathit{o}\mathit{o}\mathit{f}\mathit{s}\mathit{i}\mathit{d}\mathit{e}\mathit{s}=\mathit{n}$$$$3\times 160+(\mathit{n}-3)\times 120=(\mathit{n}-2)\times 180$$$$480-360+120\mathit{n}=180\mathit{n}-360$$$$60\mathit{n}=480\Rightarrow \mathit{n}=7$$$$\mathit{n}\mathit{o}\mathit{o}\mathit{f}\mathit{s}\mathit{i}\mathit{d}\mathit{e}\mathit{s}=7$$

Commented by pete last updated on 31/May/21

$$\mathrm{thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{sir}$$

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