Question Number 165015 by MathsFan last updated on 24/Jan/22
Commented by MathsFan last updated on 24/Jan/22
$${help}\:{please} \\ $$
Commented by MathsFan last updated on 25/Jan/22
$${thank}\:{you}\:{sir} \\ $$
Answered by mr W last updated on 25/Jan/22
Commented by mr W last updated on 25/Jan/22
$${make}\:{BE}={BC} \\ $$$${then}\:\Delta{BED}\equiv\Delta{BCD} \\ $$$${DE}={DC} \\ $$$${AE}={AB}−{EB}=\left({BC}+{CD}\right)−{BC}={CD}={DE} \\ $$$$\Rightarrow\angle{ADE}=\angle{DAE}=\alpha \\ $$$$\angle{DEB}=\mathrm{2}\alpha \\ $$$$\angle{BCD}=\angle{DEB}=\mathrm{2}\alpha \\ $$$$\angle{A}+\angle{C}+\angle{B}=\mathrm{180}° \\ $$$$\alpha+\mathrm{2}\alpha+\left(\mathrm{30}°+\mathrm{30}°\right)=\mathrm{180}° \\ $$$$\mathrm{3}\alpha=\mathrm{120}° \\ $$$$\Rightarrow\alpha=\mathrm{40}° \\ $$
Commented by Tawa11 last updated on 25/Jan/22
$$\mathrm{Great}\:\mathrm{sir} \\ $$
Answered by UC last updated on 25/Jan/22
$$\mathrm{40}° \\ $$