Quantitative Aptitude Ques 1569
Question: In the given figure, ABCD is a trapezium. EF is parallel to AD and BC. Then, $ \angle y $ is equal to [CDS 2012]
Options:
A) $ 30{}^\circ $
B) $ 45{}^\circ $
C) $ 60{}^\circ $
D) $ 65{}^\circ $
Show Answer
Answer:
Correct Answer: C
Solution:
- From figure,
$ x{}^\circ =z{}^\circ =50{}^\circ $ [alternate interior angles] $ \theta +z{}^\circ =180{}^\circ $ [linear pair]
$ \theta =180{}^\circ -50{}^\circ =130{}^\circ $ Now, in quadrilateral AQFD, $ x{}^\circ +y{}^\circ +120{}^\circ +\theta =360{}^\circ $ [ $ \therefore $ the sum of all angles in a quadrilateral is equal to $ 360{}^\circ $ ]
$ \Rightarrow $ $ 50{}^\circ +y{}^\circ +120{}^\circ +130{}^\circ =360{}^\circ $
$ \therefore $ $ y=360{}^\circ -300{}^\circ =60{}^\circ $
BETA
