Question Number 52082 by ajfour last updated on 03/Jan/19
Commented by ajfour last updated on 03/Jan/19
$${Express}\:\boldsymbol{\alpha}\:{in}\:{terms}\:{of}\:\boldsymbol{\theta}. \\ $$
Answered by mr W last updated on 03/Jan/19
$$\mathrm{4}\alpha+\mathrm{2}\beta=\pi\:\:\:\:...\left({i}\right) \\ $$$$\beta=\mathrm{2}\gamma\:\:\:\:\:...\left({ii}\right) \\ $$$$\theta=\mathrm{4}\alpha+\gamma\:\:\:...\left({iii}\right) \\ $$$$\left({i}\right)−\mathrm{2}\left({ii}\right)+\mathrm{4}\left({iii}\right): \\ $$$$\mathrm{4}\alpha+\mathrm{4}\theta=\pi+\mathrm{16}\alpha \\ $$$$\Rightarrow\alpha=\frac{\theta}{\mathrm{3}}+\frac{\pi}{\mathrm{12}} \\ $$
Commented by ajfour last updated on 03/Jan/19
$${Thank}\:{you}\:{sir}! \\ $$