Question Number 100522 by bemath last updated on 27/Jun/20
Answered by bramlex last updated on 27/Jun/20
Commented by bramlex last updated on 27/Jun/20
$$\left(\mathrm{1}\right)\pi−\alpha\:+\:\pi−\beta\:+\:{x}\:+\:{y}\:=\:\mathrm{2}\pi \\ $$$${x}+{y}=\:\alpha\:+\:\beta \\ $$$$\left(\mathrm{2}\right)\:\alpha\:+\:{y}\:+\:\beta\:=\:\mathrm{180}^{{o}} \\ $$$$\Rightarrow\alpha+\beta\:=\:\mathrm{180}^{{o}} −{y} \\ $$$${then}\:{x}+{y}\:=\:\mathrm{180}^{{o}} −{y} \\ $$$$\Leftrightarrow\:{x}+\mathrm{2}{y}\:=\:\mathrm{180}^{{o}} \\ $$
Commented by bemath last updated on 27/Jun/20
$$\mathrm{thank}\:\mathrm{you} \\ $$