Question

In the given figure, if $\angle BAC={90}^{\circ },\angle BAD=\angle CAD$ and $\angle DAE=\angle CAE$ find $\angle BAE$

• A. ${62.5}^{\circ }$
• B. $67{\frac{1}{2}}^{\circ }$
• C. ${75}^{\circ }$
• D. $77{\frac{1}{2}}^{\circ }$

Answer 1

Answer: (A)

${62.5}^{\circ }$

$\angle CAB={90}^{\circ }=\angle CAD+\angle DAB(\because \angle CAD=\angle DAB)$

$\Rightarrow \angle CAD={45}^{\circ }=\angle CAE+\angle EAD$

$\Rightarrow \angle EAD={22.5}^{\circ }[\because \angle CAE=\angle EAD]$

$\Rightarrow \angle BAE=\angle EAD+\angle DAB=67.5$