MCQ
In the given figure, $AB \| CD$. If $\text{AOC}=30^\circ$ and $\angle\text{OAB}=100^\circ$ then $\angle\text{OCD}=?$ 
- A$150^\circ$
- B$80^\circ$
- ✓$130^\circ$
- D$100^\circ$
✓
Answer
Correct option: C.
$130^\circ$
Draw $OE \| AB \| CD$
Now, $OE \| AB$ and $OA$ is the transversal.
$\therefore\angle\text{OAB}+\angle\text{AOE}=180^\circ$ [Angles on the same side of a transversal line are supplementary]
$\Rightarrow\angle\text{OAB}+\angle\text{AOC}+\angle\text{COE}=180^\circ$
$\Rightarrow100^\circ+30^\circ+\angle\text{COE}=180^\circ$
$\Rightarrow\angle\text{COE}=50^\circ$
Also,
$OE \| CD$ and $OC$ is the transversal.
$\therefore\angle\text{OCD}+\angle\text{COE}=180^\circ$ [Angles on the same side of a transversal line are supplementary]
$\Rightarrow\angle\text{OCD}+50^\circ=180^\circ$
$\Rightarrow\angle\text{OCD}=130^\circ.$
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