Question

In the given figure, AB || CD. If ∠AOC = 30° and ∠OAB = 100°, then ∠OCD = ?
(a) 130°
(b) 150°
(c) 80°
(d) 100°

Answer 1

(a) 130°

Draw $OE\parallel AB\parallel CD$
Now, $OE\parallel AB\text{and}OA$ is the transversal.
$$\begin{gathered} \therefore \angle OAB+\angle AOE=180°\left[\text{Angles on the same side of a transversal line are supplementary}\right] \\ \Rightarrow \angle OAB+\angle AOC+\angle COE=180° \\ \Rightarrow 100°+30°+\angle COE=180° \\ \Rightarrow \angle COE=50° \end{gathered}$$
Also,
$OE\parallel CD\text{and}OC$ is the transversal.
$$\begin{gathered} \therefore \angle OCD+\angle COE=180°\left[\text{Angles on the same side of a transversal line are supplementary}\right] \\ \Rightarrow \angle OCD+50°=180° \\ \Rightarrow \angle OCD=\mathbf{130}\mathbf{°} \end{gathered}$$