Quantitative Aptitude Ques 2441
Question: In the given figure, $ AB\parallel CD. $ If $ \angle AOC=30{}^\circ $ and $ \angle OAB=100{}^\circ , $ then $ \angle OCD $ is equal to
Options:
A) $ 130{}^\circ $
B) $ 150{}^\circ $
C) $ 80{}^\circ $
D) $ 100{}^\circ $
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Answer:
Correct Answer: A
Solution:
- Let $ \angle OCD=x{}^\circ $ Draw $ OE\parallel AB\parallel CD $ Now, $ AB\parallel OE $ and OA is the transversal.
$ \therefore $ $ \angle OAB+\angle AOE=180{}^\circ $
$ \Rightarrow $ $ \angle BAO+\angle AOC+\angle COE=180{}^\circ $
$ \Rightarrow $ $ 100{}^\circ +30{}^\circ +\angle COE=180{}^\circ $
$ \Rightarrow $ $ \angle COE=50{}^\circ $
Again, $ CD||OE $ and OC is transversal.
$ \Rightarrow $ $ \angle OCD+\angle EOC=180{}^\circ $
$ \Rightarrow $ $ x=130{}^\circ $
BETA
