Quantitative Aptitude Ques 1334
Question: In the given figure, XV is parallel to PQ. Find the value of the angles marked x and y.
Options:
A) $ 27{}^\circ , $ $ 17{}^\circ $
B) $ 45{}^\circ , $ $ 25{}^\circ $
C) $ 70{}^\circ , $ $ 30{}^\circ $
D) $ 36{}^\circ , $ $ 16{}^\circ $
Show Answer
Answer:
Correct Answer: C
Solution:
- $ \angle EAY+\angle YAO+\angle OAB=180{}^\circ $ [linear pair]
$ \Rightarrow $ $ 60{}^\circ +40{}^\circ +\angle OAB=180{}^\circ $
$ \Rightarrow $ $ \angle OAB=80{}^\circ $ $ XY||PQ $ and AB is the transversal. $ \angle EAY=\angle ABQ $ [corresponding angles]
$ \Rightarrow $ $ \angle EAY=\angle ABO+\angle OBQ $
$ \Rightarrow $ $ 60{}^\circ =30{}^\circ +y $
$ \Rightarrow $ $ y=30{}^\circ $ In $ \Delta AOB, $ $ \angle AOB+\angle OBA+\angle BAO=180{}^\circ $ $ x+30{}^\circ +80{}^\circ =180{}^\circ $
$ \Rightarrow $ $ x=70{}^\circ $
$ \Rightarrow $ $ x=70{}^\circ $ and $ y=30{}^\circ $
BETA
