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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

(1)π−α + π−β + x + y = 2π  x+y= α + β  (2) α + y + β = 180^o   ⇒α+β = 180^o −y  then x+y = 180^o −y  ⇔ x+2y = 180^o

$$\left(\mathrm{1}\right)\pi−\alpha\:+\:\pi−\beta\:+\:{x}\:+\:{y}\:=\:\mathrm{2}\pi \\ $$$${x}+{y}=\:\alpha\:+\:\beta \\ $$$$\left(\mathrm{2}\right)\:\alpha\:+\:{y}\:+\:\beta\:=\:\mathrm{180}^{{o}} \\ $$$$\Rightarrow\alpha+\beta\:=\:\mathrm{180}^{{o}} −{y} \\ $$$${then}\:{x}+{y}\:=\:\mathrm{180}^{{o}} −{y} \\ $$$$\Leftrightarrow\:{x}+\mathrm{2}{y}\:=\:\mathrm{180}^{{o}} \\ $$

Commented by bemath last updated on 27/Jun/20

thank you

$$\mathrm{thank}\:\mathrm{you} \\ $$

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