The ratio between the adjacent angles of a parallelogram is 2 : 3 respectively. 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?

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BANK PO Exam (Union Bank of India) 2001 click here to view all questions

The ratio between the adjacent angles of a parallelogram is 2 : 3 respectively. 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?

A$252^∘$

B$226^∘$

C$144^∘$

DNone of these

Nithin ? Aug 13 '2022 at 13:6

Correct answer is: None of these

Explanation:

Let the adjacent angles of parallelogram be \(\Large 2x ^{\circ} \text{ and }\ 3x ^{\circ}\) respectively
Then, \(\Large 2x ^{\circ} + 3x ^{\circ} = 180^o\)

\(\Large 5x ^{\circ} = 180^o\)

\(x^∘=36^∘ \)

 

Smaller angle of parallelogram \(= 2x = 72^∘\)

= Smallest angle of the quadrilateral \(= 36^∘\)

 

Therefore, Its largest angle \(= 4×36=144^∘\)

 

Therefore, Required sum \(= 144 + 72 = 216^∘\)

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Correct answer is: None of these Explanation: Let the adjacent angles of parallelogram be \(\Large 2x ^{\circ} \text{ and }\ 3x ^{\circ}\) respectively Then, \(\Large 2x ^{\circ} + 3x ^{\circ} = 180^o\) \(\Large 5x ^{\circ} = 180^o\) \(x^∘=36^∘ \)   Smaller angle of parallelogram \(= 2x = 72^∘\) = Smallest angle of the quadrilateral \(= 36^∘\)   Therefore, Its largest angle \(= 4×36=144^∘\)   Therefore, Required sum \(= 144 + 72 = 216^∘\) Nithin ? answered Aug 13 '2022 at 13:6 All Comments

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