Question

In the given figure, ∠BAC = 40°, ∠ACB = 90° and ∠BED = 100°. Then ∠BDE = ?
(a) 50°
(b) 30°
(c) 40°
(d) 25°

Answer 1

(b) 30°

In $∆ABC$, we have:
$$\begin{gathered} \angle A+\angle B+\angle C=180°\left[\text{Sum of the angles of a triangle}\right] \\ \Rightarrow 40°+\angle B+90°=180° \\ \Rightarrow \angle B=50° \end{gathered}$$
In $∆EBD$, we have:
$$\begin{gathered} \angle E+\angle B+\angle D=180°\left[\text{Sum of the angles of a triangle}\right] \\ \Rightarrow 100°+50°+\angle D=180° \\ \Rightarrow \angle D=30° \\ \Rightarrow \angle BDE=30° \end{gathered}$$