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Question Number 104877 by  M±th+et+s last updated on 24/Jul/20

$$$$$$findx$$

Answered by ajfour last updated on 24/Jul/20

Commented by  M±th+et+s last updated on 24/Jul/20

$$welldonesir$$

Commented by ajfour last updated on 24/Jul/20

$$\frac{\pi }{2}+\alpha +\frac{2\pi }{5}=\pi \Rightarrow \mathit{\alpha }=\frac{\pi }{10}$$$$\beta =\frac{1}{2}(\frac{\pi }{2}+\alpha )=\frac{3\pi }{10}$$$$\sin \mathit{\varphi }=\frac{a/2}{a}\Rightarrow \mathit{\varphi }=\frac{\pi }{6}$$$$\mathit{\varphi }+\mathit{\beta }=\mathit{\pi }-2\mathit{x}$$$$\Rightarrow \mathit{x}=\frac{\mathit{\pi }}{2}-\frac{\mathit{\beta }}{2}-\frac{\mathit{\varphi }}{2}$$$$=90°-27°-15°$$$$\Rightarrow \mathit{x}=48°.$$

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