Question

In the given figure, ∠OAB = 75°, ∠OBA = 55° and ∠OCD = 100°. Then ∠ODC = ?
(a) 20°
(b) 25°
(c) 30°
(d) 35°

Answer 1

(c) 30°
In $∆OAB$, we have:
$$\begin{gathered} \angle OAB+\angle OBA+\angle AOB=180°\left[\text{Sum of the angles of a triangle}\right] \\ \Rightarrow 75°+55°+\angle AOB=180° \\ \Rightarrow \angle AOB=50° \end{gathered}$$
$\therefore \angle COD=\angle AOB=50°\left[\text{Vertically-Opposite Angles}\right]$
In $∆OCD$, we have:
$$\begin{gathered} \angle COD+\angle OCD+\angle ODC=180°\left[\text{Sum of the angles of a triangle}\right] \\ \Rightarrow 50°+100°+\angle ODC=180° \\ \Rightarrow \angle ODC=30° \end{gathered}$$