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Question Number 165015 by MathsFan last updated on 24/Jan/22

Commented by MathsFan last updated on 24/Jan/22

help please

$${help}\:{please} \\ $$

Commented by MathsFan last updated on 25/Jan/22

thank you sir

$${thank}\:{you}\:{sir} \\ $$

Answered by mr W last updated on 25/Jan/22

Commented by mr W last updated on 25/Jan/22

make BE=BC then ΔBED≡ΔBCD DE=DC AE=AB−EB=(BC+CD)−BC=CD=DE ⇒∠ADE=∠DAE=α ∠DEB=2α ∠BCD=∠DEB=2α ∠A+∠C+∠B=180° α+2α+(30°+30°)=180° 3α=120° ⇒α=40°

$${make}\:{BE}={BC} \\ $$$${then}\:\Delta{BED}\equiv\Delta{BCD} \\ $$$${DE}={DC} \\ $$$${AE}={AB}−{EB}=\left({BC}+{CD}\right)−{BC}={CD}={DE} \\ $$$$\Rightarrow\angle{ADE}=\angle{DAE}=\alpha \\ $$$$\angle{DEB}=\mathrm{2}\alpha \\ $$$$\angle{BCD}=\angle{DEB}=\mathrm{2}\alpha \\ $$$$\angle{A}+\angle{C}+\angle{B}=\mathrm{180}° \\ $$$$\alpha+\mathrm{2}\alpha+\left(\mathrm{30}°+\mathrm{30}°\right)=\mathrm{180}° \\ $$$$\mathrm{3}\alpha=\mathrm{120}° \\ $$$$\Rightarrow\alpha=\mathrm{40}° \\ $$

Commented by Tawa11 last updated on 25/Jan/22

Great sir

$$\mathrm{Great}\:\mathrm{sir} \\ $$

Answered by UC last updated on 25/Jan/22

40°

$$\mathrm{40}° \\ $$

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