SATHEE: Quantitative Aptitude Ques 1221

Quantitative Aptitude Ques 1221

Question: In the given figure, $ AB||CD $ and they cut PQ and QR at E, F and G, H, respectively. $ \angle PEB=70{}^\circ $ and $ \angle QHD=140{}^\circ $ and $ \angle PQR=x. $ Find the value of x.

Options:

A) $ 20{}^\circ $

B) $ 30{}^\circ $

C) $ 24{}^\circ $

D) $ 32{}^\circ $

Show Answer

Answer:

Correct Answer: B

Solution:

Since, $ AB||CD $ and PQ is the transversal.

$ \therefore $ $ \angle PEF=\angle EGH $ [corresponding angles] $ \angle EGH=70{}^\circ $ $ [\because \angle PEF=70{}^\circ ] $ $ \angle EGH+\angle HGQ=180{}^\circ $ [linear pair]

$ \Rightarrow $ $ \angle HGQ=180{}^\circ -70{}^\circ =110{}^\circ $ $ \angle DHQ+\angle GHQ=180{}^\circ $ [linear pair]

$ \Rightarrow $ $ \angle GHQ=180{}^\circ -140{}^\circ =40{}^\circ $ In $ \Delta GQH, $ $ \angle GQH+\angle GHQ+\angle HGQ=180{}^\circ $

$ \Rightarrow $ $ x+40{}^\circ +110{}^\circ =180{}^\circ $

$ \Rightarrow $ $ x+150{}^\circ =180{}^\circ $
$ \Rightarrow $ $ x=30{}^\circ $

Quantitative Aptitude Ques 1220

Quantitative Aptitude Ques 1222

Quantitative Aptitude Ques 1221

Question: In the given figure, $ AB||CD $ and they cut PQ and QR at E, F and G, H, respectively. $ \angle PEB=70{}^\circ $ and $ \angle QHD=140{}^\circ $ and $ \angle PQR=x. $ Find the value of x.

Options:

Answer:

Solution:

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