Question Number 68132 by mr W last updated on 05/Sep/19
Commented by kaivan.ahmadi last updated on 05/Sep/19
$${a}+\beta+\theta=\mathrm{180}\:\:\:\left(\mathrm{1}\right) \\ $$$$\alpha+\beta−{a}=\mathrm{0}\:\:\:\:\:\left(\mathrm{2}\right) \\ $$$$\mathrm{2}\alpha−\mathrm{2}\theta+{b}=\mathrm{0}\:\:\:\left(\mathrm{3}\right) \\ $$$$\left(\mathrm{3}\right)−\left(\mathrm{2}\right):\:\alpha−\mathrm{2}\theta−\beta+\left({a}+{b}\right)=\mathrm{0}\Rightarrow\mathrm{2}\theta+\beta−\alpha=\mathrm{120}\:\:\:\left(\mathrm{4}\right) \\ $$$$\left(\mathrm{1}\right)−\left(\mathrm{2}\right):\:\mathrm{2}{a}+\theta−\alpha=\mathrm{180} \\ $$$$\left(\mathrm{1}\right)+\left(\mathrm{3}\right):\:\mathrm{2}\alpha+\beta−\theta+\left({a}+{b}\right)=\mathrm{180}\Rightarrow\mathrm{2}\alpha+\beta−\theta=\mathrm{60}\:\:\:\left(\mathrm{5}\right) \\ $$$$\mathrm{2}\left(\mathrm{5}\right)+\left(\mathrm{4}\right):\:\mathrm{3}\alpha+\mathrm{3}\beta=\mathrm{240}\Rightarrow\alpha+\beta=\mathrm{80}\:\:\left(\mathrm{6}\right) \\ $$$${from}\:\left(\mathrm{2}\right)\:{and}\:\left(\mathrm{6}\right){we}\:{have}\:\mathrm{80}−{a}=\mathrm{0}\Rightarrow{a}=\mathrm{80} \\ $$$$ \\ $$
Commented by mr W last updated on 06/Sep/19
$${thank}\:{you}! \\ $$
Commented by TawaTawa last updated on 06/Sep/19
$$\mathrm{Great},\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{I}\:\mathrm{understand} \\ $$