Quantitative Aptitude Ques 892
Question: The ratio between the adjacent angles of a parallelogram is 2: 3. Half the smaller angle of the parallelogram is equal to the smallest angle of a quadrilateral. Largest angle of quadrilateral is four times its smallest angle.
What is the sum of largest angle of quadrilateral and the smaller angle of parallelogram?
Options:
A) $ 252{}^\circ $
B) $ 226{}^\circ $
C) $ 144{}^\circ $
D) $ 180{}^\circ $
E) None of these
Show Answer
Answer:
Correct Answer: E
Solution:
- Let the adjacent angles of parallelogram be $ 2x $ and $ 3x, $ respectively. Then, $ 2x+3x=180{}^\circ $
$ \Rightarrow $ $ 5x=180{}^\circ $
$ \Rightarrow $ $ x=36{}^\circ $
$ \therefore $ Smaller angle, $ 2x=72{}^\circ $
$ \therefore $ Smallest angle of quadrilateral $ =36{}^\circ $
$ \therefore $ Its largest angle $ =4\times 36{}^\circ =144{}^\circ $ Hence, required sum $ =144{}^\circ +72{}^\circ =216{}^\circ $
BETA
