SATHEE: Quantitative Aptitude Ques 892

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 $

Quantitative Aptitude Ques 891

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