Lines and Angles — MATHS STD 7 — Question

 Construction: Draw a line $OE$ from the point $O$ parallel to $AB$ and $CD$

Since, $AB || OE$
$\therefore\angle \text{BAO}+\angle \text{AOE}=180^\circ$ [Angles on the same side of a transversal line are supplementary]
$\Rightarrow 150^\circ+\angle \text{AOE}=180^\circ$
$\Rightarrow \angle \text{AOE}=30^\circ$
Again, $CD || OE$
$\therefore \angle \text{DCO}+\angle \text{COE}=180^\circ$ [Angles on the same side of a transversal line are supplementary]
$\Rightarrow 120^\circ+\angle \text{COE}=180^\circ$
$\Rightarrow \angle \text{COE}=60^\circ$
Now, $\angle \text{AOC}=\angle \text{AOE}+\angle \text{COE}$
$=30^\circ+60^\circ$
$=90^\circ$
Hence, the correct answer is option $(b).$