Question

In the given figure, AB || CD. If ∠BAO = 110°, ∠AOC = 20° and ∠OCD = x°, find the value of x.
Figure

Answer 1

Draw $OE\parallel AB\parallel CD$.
Now, $OE\parallel AB\text{and}OA$ is the transversal.
$$\begin{gathered} \therefore \angle OAB+\angle AOE=180°\left[\text{Sum of consecutive interior angles is supplementary}\right] \\ \Rightarrow \angle OAB+\angle AOC+\angle COE=180° \\ \Rightarrow 110°+20°+\angle COE=180° \\ \Rightarrow \angle COE=50° \end{gathered}$$
Also,
$OE\parallel CD\text{and}OC$ is the transversal.
$$\begin{gathered} \therefore \angle OCD+\angle COE=180°\left[\text{Sum of consecutive interior angles is supplementary}\right] \\ \Rightarrow x°+50°=180° \\ \Rightarrow x°=130° \\ \mathrm{Therefore},x=130 \end{gathered}$$