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Question-165015




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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