Question

In ∆ABC, BD ⊥ AC, ∠CAE = 30° and ∠CBD = 40°. Then, ∠AEB = ?
(a) 70°
(b) 80°
(c) 50°
(d) 60°

Answer 1

(b) 80°

In $∆BCD$, we have:
$$\begin{gathered} \angle CBD+\angle BDC+\angle BCD=180°\left[\text{Sum of the angles of a triangle}\right] \\ \Rightarrow 40°+90°+\angle BCD=180° \\ \Rightarrow \angle BCD=50° \\ \Rightarrow \angle ECD=50° \end{gathered}$$
Side CE of triangle AEC is produced to B.
$$\begin{gathered} \therefore \angle AEB=\angle EAC+\angle ACE \\ \Rightarrow \angle AEB=30°+50° \\ \Rightarrow \angle AEB=80° \end{gathered}$$