Question

In the given figure, ∠CDE = ${60}^{\circ }$ and ∠CED = ${90}^{\circ }$. Find the values of ∠CAD and ∠CBE.

• A. ${30}^{\circ }$ and ${45}^{\circ }$
• B. ${60}^{\circ }$ and ${90}^{\circ }$
• C. ${15}^{\circ }$ and ${30}^{\circ }$
• D. ${45}^{\circ }$and ${60}^{\circ }$

Answer 1

The correct option is A ${30}^{\circ }$ and ${45}^{\circ }$

∠PAD =${60}^{\circ }$ , ∠QBE = ${90}^{\circ }$
∠CAD = $\frac{\angle PAD}{2}$ = ${30}^{\circ }$ [AC angle bisector]
∠CBE = $\frac{\angle QBE}{2}$ =${45}^{\circ }$ [BC angle bisector]