Question

The sides BC, BA and CA of ∆ABC have been produced to D, E and F, respectively, as shown in the given figure. Then, ∠B = ?
(a) 35°
(b) 55°
(c) 65°
(d) 75°

Answer 1

(d) 75°

We have:
$\angle BAC=\angle EAF=35°\left[\text{Vertically-Opposite Angles}\right]$
Side CD of triangle ABC is produced to D.
$$\begin{gathered} \therefore \angle ACD=\angle BAC+\angle ABC \\ \Rightarrow 110°=35°+\angle ABC \\ \Rightarrow \angle ABC=75° \\ \Rightarrow \angle B=75° \end{gathered}$$