SATHEE: Quantitative Aptitude Ques 508

Quantitative Aptitude Ques 508

Question: AB is a straight line and O is a point lying on AB. A line OC is drawn from O such that $ \angle COA=36{}^\circ . $ OD is a line within the $ \angle COA $ such that $ \angle DOA=( \frac{1}{3} )\angle COA. $ If OE is a line within the $ \angle BOC, $ $ \angle BOE=( \frac{1}{4} )\angle BOC, $ then the $ \angle DOE $ must be

Options:

A) $ 60{}^\circ $

B) $ 45{}^\circ $

C) $ 36{}^\circ $

D) $ 80{}^\circ $

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Answer:

Correct Answer: A

Solution:

[a] $ \angle DOA=\frac{1}{3}\angle COA $ and $ \angle BOE=\frac{1}{4}\angle BOC $

$ \therefore $ $ \angle DOC=\frac{2}{3}\angle COA $ and $ \angle COE=\frac{3}{4},\angle BOC $

$ \Rightarrow $ $ \angle DOC=\frac{2}{3}\times 36{}^\circ =24{}^\circ $ and $ \angle COE=\frac{1}{4}(180{}^\circ -36{}^\circ )=\frac{1}{4}\times 144{}^\circ =36{}^\circ $

$ \therefore $ $ \angle DOE=\angle DOC+\angle COE=24{}^\circ +36{}^\circ =60{}^\circ $

Quantitative Aptitude Ques 507

Quantitative Aptitude Ques 509

Quantitative Aptitude Ques 508

Options:

Answer:

Solution:

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