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Question Number 68132 by mr W last updated on 05/Sep/19

Commented by kaivan.ahmadi last updated on 05/Sep/19

a+β+θ=180 (1) α+β−a=0 (2) 2α−2θ+b=0 (3) (3)−(2): α−2θ−β+(a+b)=0⇒2θ+β−α=120 (4) (1)−(2): 2a+θ−α=180 (1)+(3): 2α+β−θ+(a+b)=180⇒2α+β−θ=60 (5) 2(5)+(4): 3α+3β=240⇒α+β=80 (6) from (2) and (6)we have 80−a=0⇒a=80

$${a}+\beta+\theta=\mathrm{180}\:\:\:\left(\mathrm{1}\right) \\ $$$$\alpha+\beta−{a}=\mathrm{0}\:\:\:\:\:\left(\mathrm{2}\right) \\ $$$$\mathrm{2}\alpha−\mathrm{2}\theta+{b}=\mathrm{0}\:\:\:\left(\mathrm{3}\right) \\ $$$$\left(\mathrm{3}\right)−\left(\mathrm{2}\right):\:\alpha−\mathrm{2}\theta−\beta+\left({a}+{b}\right)=\mathrm{0}\Rightarrow\mathrm{2}\theta+\beta−\alpha=\mathrm{120}\:\:\:\left(\mathrm{4}\right) \\ $$$$\left(\mathrm{1}\right)−\left(\mathrm{2}\right):\:\mathrm{2}{a}+\theta−\alpha=\mathrm{180} \\ $$$$\left(\mathrm{1}\right)+\left(\mathrm{3}\right):\:\mathrm{2}\alpha+\beta−\theta+\left({a}+{b}\right)=\mathrm{180}\Rightarrow\mathrm{2}\alpha+\beta−\theta=\mathrm{60}\:\:\:\left(\mathrm{5}\right) \\ $$$$\mathrm{2}\left(\mathrm{5}\right)+\left(\mathrm{4}\right):\:\mathrm{3}\alpha+\mathrm{3}\beta=\mathrm{240}\Rightarrow\alpha+\beta=\mathrm{80}\:\:\left(\mathrm{6}\right) \\ $$$${from}\:\left(\mathrm{2}\right)\:{and}\:\left(\mathrm{6}\right){we}\:{have}\:\mathrm{80}−{a}=\mathrm{0}\Rightarrow{a}=\mathrm{80} \\ $$$$ \\ $$

Commented by mr W last updated on 06/Sep/19

thank you!

$${thank}\:{you}! \\ $$

Commented by TawaTawa last updated on 06/Sep/19

Great, God bless you sir. I understand

$$\mathrm{Great},\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{I}\:\mathrm{understand} \\ $$

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