Question Number 104877 by M±th+et+s last updated on 24/Jul/20
$$ \\ $$$${find}\:{x} \\ $$
Answered by ajfour last updated on 24/Jul/20
Commented by M±th+et+s last updated on 24/Jul/20
$${well}\:{done}\:{sir} \\ $$
Commented by ajfour last updated on 24/Jul/20
$$\frac{\pi}{\mathrm{2}}+\alpha+\frac{\mathrm{2}\pi}{\mathrm{5}}=\pi\:\:\:\Rightarrow\:\:\boldsymbol{\alpha}=\frac{\pi}{\mathrm{10}} \\ $$$$\beta=\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\pi}{\mathrm{2}}+\alpha\right)=\frac{\mathrm{3}\pi}{\mathrm{10}} \\ $$$$\mathrm{sin}\:\boldsymbol{\phi}=\frac{{a}/\mathrm{2}}{{a}}\:\:\:\:\Rightarrow\:\:\boldsymbol{\phi}=\frac{\pi}{\mathrm{6}} \\ $$$$\boldsymbol{\phi}+\boldsymbol{\beta}\:=\:\boldsymbol{\pi}−\mathrm{2}\boldsymbol{{x}} \\ $$$$\Rightarrow\:\:\:\boldsymbol{{x}}=\frac{\boldsymbol{\pi}}{\mathrm{2}}−\frac{\boldsymbol{\beta}}{\mathrm{2}}−\frac{\boldsymbol{\phi}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{90}°−\mathrm{27}°−\mathrm{15}° \\ $$$$\:\:\:\:\:\:\Rightarrow\:\:\:\boldsymbol{{x}}\:=\:\mathrm{48}°\:. \\ $$