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Question Number 197196 by sonukgindia last updated on 10/Sep/23

Answered by mahdipoor last updated on 10/Sep/23

$$blue\equiv$$$$\pi r^2(\frac{{\alpha }_1}{360}+\frac{{\alpha }_2}{360}+\frac{{\alpha }_3}{360}...+\frac{{\alpha }_n}{360})$$$$orange\equiv$$$$\pi r^2(\frac{360-{\alpha }_1}{360}+\frac{360-{\alpha }_2}{360}+\frac{360-{\alpha }_3}{360}...+\frac{360-{\alpha }_n}{360})$$$$O-B=\pi r^2(n-2\frac{\mathrm{\Sigma }\alpha }{360})=\pi r^2(n-2\frac{180\times (n-2)}{360})$$$$=2\pi r^2$$$$$$

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