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Question Number 142326 by bramlexs22 last updated on 30/May/21

Answered by EDWIN88 last updated on 30/May/21

$$\frac{180(\mathrm{n}-2)}{\mathrm{n}}=4\left(\frac{\cancel{180}{}^{36}}{\cancel{5}}\right)$$$$\frac{180\mathrm{n}-360}{\mathrm{n}}=144\Rightarrow 180\mathrm{n}-360=144\mathrm{n}$$$$\Rightarrow 36\mathrm{n}=360;\mathrm{n}=10$$$$$$

Answered by Rasheed.Sindhi last updated on 30/May/21

$$Forn-gon$$$${}^{\bullet }Sumofinteriorangles=180(n-2)$$$${}^{\bullet }Sumofexteriorangles=360$$$$\left(constantforallpolygons\right)$$$$180(n-2)=4\times 360$$$$180n=4\times 360+360=5\times 360$$$$n=\frac{5\times \cancel{\stackrel{2}{360}}}{\cancel{180}}=10$$

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