Question

In the given figure, AB || CD. If ∠EAB = 50° and ∠ECD = 60°, then ∠AEB = ?
(a) 50°
(b) 60°
(c) 70°
(d) 55°

Answer 1

(c) 70°

$AB\parallel CD\text{and}BC$ is the transversal.
$\therefore \angle ABE=\angle BCD=60°\left[\text{Alternate Internal Angles}\right]$
In $∆ABE$, we have:
$$\begin{gathered} \angle EAB+\angle ABE+\angle AEB=180°\left[\text{Sum of the angles of a triangle}\right] \\ \Rightarrow 50°+60°+\angle AEB=180° \\ \Rightarrow \angle AEB=70° \end{gathered}$$