SATHEE: Quantitative Aptitude Ques 1749

Quantitative Aptitude Ques 1749

Question: The angles $ x{}^\circ , $ $ a{}^\circ , $ $ c{}^\circ $ and $ (\pi -b{}^\circ ) $ are indicated in the figure given below. Which one of the following is correct?

Options:

A) $ x{}^\circ =a{}^\circ +c{}^\circ -b{}^\circ $

B) $ x{}^\circ =b{}^\circ -a{}^\circ -c{}^\circ $

C) $ x{}^\circ =a{}^\circ +b{}^\circ +c{}^\circ $

D) $ x{}^\circ =a{}^\circ -b{}^\circ +c{}^\circ $

Show Answer

Answer:

Correct Answer: C

Solution:

$ \because $ $ \angle PCT+\angle PCB=\pi $ [linear pair]
$ \angle PCB=\pi -(\pi -b{}^\circ )=b{}^\circ $ … (i) In $ \Delta BPC, $
$ \angle PCB+\angle BPC+\angle PBC=\pi $

$ \Rightarrow $ $ \angle PBC=\pi -\angle PCB+\angle BPC $ $ =\pi -b{}^\circ -a{}^\circ $ (ii) $ \because $ $ \angle ABE+\angle EBC=\pi $ $ [\because \angle PBC=\angle EBC] $ [linear pair]

$ \Rightarrow $ $ \angle ABE=\pi -\angle PBC=\pi -(\pi -b{}^\circ -a{}^\circ ) $ $ =a{}^\circ +b{}^\circ $ (iii) Now, in $ \Delta ABE, $ Sum of two interior angles = Exterior angle $ \angle EAB+\angle ABE=\angle BES $

$ \Rightarrow $ $ c{}^\circ +b{}^\circ +a{}^\circ =x{}^\circ $

$ \therefore $ $ x{}^\circ =a{}^\circ +b{}^\circ +c{}^\circ $

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Quantitative Aptitude Ques 1749

Question: The angles $ x{}^\circ , $ $ a{}^\circ , $ $ c{}^\circ $ and $ (\pi -b{}^\circ ) $ are indicated in the figure given below. Which one of the following is correct?

Options:

Answer:

Solution:

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