SATHEE: Quantitative Aptitude Ques 906

Quantitative Aptitude Ques 906

Question: An equilateral $ \Delta TQR $ is drawn inside a square PQRS. The value of the angle PTS, in degrees) is

Options:

A) 120

B) 150

C) 75

D) 90

Show Answer

Answer:

Correct Answer: B

Solution:

Since, $ \Delta TQR $ is an equilateral triangle.

$ \therefore $ $ \angle TQR=\angle TRQ=\angle RTQ=60{}^\circ $ and $ TQ=TR=RQ $ and $ SR=RQ=PQ=SP $ [sides of square] Now, in $ \Delta RTS $ $ RT=SR $

$ \therefore $ $ \angle STR=RST $ (angle opposite to equal sides are equal] $ =\frac{180{}^\circ -30{}^\circ }{2}=75{}^\circ $ Similarly, in $ \Delta QTP, $ $ QT=PQ $ $ \angle PTQ=\angle QPT=75{}^\circ $ Now, at point T $ \angle PTS+\angle PTQ+\angle QTR+\angle RTS=360{}^\circ $ [since, angles around on point is equal to $ 360{}^\circ $ ]

$ \Rightarrow $ $ \angle PTS=360{}^\circ -(75{}^\circ +60{}^\circ +75{}^\circ ) $ $ =360{}^\circ -210{}^\circ =150{}^\circ $

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Quantitative Aptitude Ques 906

Question: An equilateral $ \Delta TQR $ is drawn inside a square PQRS. The value of the angle PTS, in degrees) is

Options:

Answer:

Solution:

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