Question

In the given figure, AB || CD. If ∠BAO = 60° and ∠OCD = 110°, then ∠AOC = ?
(a) 70°
(b) 60°
(c) 50°
(d) 40°

Answer 1

(c) 50°

Draw $EOF\parallel AB\parallel CD$.
Now, $EO\parallel AB\text{and}OA$ is the transversal.
$\therefore \angle EOA=\angle OAB=60°\left[\text{Alternate Interior Angles}\right]$
Also,
$OF\parallel CD\text{and}OC$ is the transversal.
$$\begin{gathered} \therefore \angle COF+\angle OCD=180°\left[\text{Angles on the same side of a transversal line are supplementary}\right] \\ \Rightarrow \angle COF+110°=180° \\ \Rightarrow \angle COF=70° \end{gathered}$$
Now,
$$\begin{gathered} \angle EOA+\angle AOC+\angle COF=180°\left[\because EOF\text{is a straight line}\right] \\ \Rightarrow 60°+\angle AOC+70°=180° \\ \Rightarrow \angle AOC=\mathbf{50}\mathbf{°} \end{gathered}$$