Question

In the given figure, AB || CD. If ∠OAB = 124° and ∠OCD = 136°, then ∠AOC = ?
(a) 80°
(b) 90°
(c) 100°
(d) 110°

Answer 1

(c) 100°

Draw $OL\parallel AB\parallel CD$.
Now, $OL\parallel AB\text{and}OA$ is the transversal.
$$\begin{gathered} \angle AOL+\angle OAB=180°\left[\text{Angles on the same side of a transversal line are supplementary}\right] \\ \Rightarrow \angle AOL+124°=180° \\ \Rightarrow \angle AOL=56° \end{gathered}$$
Also,
$OL\parallel CD\text{and}OC$ is the transversal.
$$\begin{gathered} \therefore \angle DCO+\angle COL=180°\text{Angles on the same side of a transversal line are supplementary} \\ \Rightarrow 136°+\angle COL=180° \\ \Rightarrow \angle COL=44° \end{gathered}$$
Therefore,
$$\begin{gathered} \angle AOC=\angle AOL+\angle COL \\ \Rightarrow \angle AOC=\left(56+44\right)° \\ \Rightarrow \angle AOC=\mathbf{100}\mathbf{°} \end{gathered}$$