SATHEE: Quantitative Aptitude Ques 1226

Quantitative Aptitude Ques 1226

Question: In the given figure, $ CD||AB. $ Find y.

Options:

A) $ 79{}^\circ $

B) $ 72{}^\circ $

C) $ 74{}^\circ $

D) $ 74{}^\circ $

Show Answer

Answer:

Correct Answer: B

Solution:

In $ \Delta ABC, $ $ \angle ABC+\angle BCA+\angle CAB=180{}^\circ $

$ \Rightarrow $ $ 4x+3x+3x=180{}^\circ $
$ \Rightarrow $ $ x=18{}^\circ $ $ AB||CD $ and $ BC $ is the transversal, then $ \angle ABC+\angle BCD=180{}^\circ $ [sum of the internal angles on the same side of the transversal]

$ \Rightarrow $ $ \angle ABC+\angle BCA+\angle ACD=180{}^\circ $

$ \Rightarrow $ $ 4x+3x+\angle ACD=180{}^\circ $

$ \Rightarrow $ $ \angle ACD=180{}^\circ -7x $

$ \Rightarrow $ $ \angle ACD=180{}^\circ -7\times 18{}^\circ =54{}^\circ $ Also, $ \angle ACE=\angle CAB+\angle ABC $ exterior angle is equal to the sum of interior opposite angles. $ \angle ACD+\angle DCE=3x+4x=7x $

$ \Rightarrow $ $ 54{}^\circ +y=7\times 18{}^\circ =126{}^\circ $

$ \Rightarrow $ $ y=126{}^\circ -54{}^\circ =72{}^\circ $

Quantitative Aptitude Ques 1225

Quantitative Aptitude Ques 1227

Quantitative Aptitude Ques 1226

Question: In the given figure, $ CD||AB. $ Find y.

Options:

Answer:

Solution:

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