One of the angles of a quadrilateral is thrice the smaller angle of a parallelogram. The respective ratio between the adjacent angles of the parallelogram is 4:5. Remaining three angles of the quadrilateral are in ratio 4 : 11 : 9 respectively. What is the sum of the largest and the smallest angles of the quadrilateral?
One of the angles of a quadrilateral is thrice the smaller angle of a parallelogram. The respective ratio between the adjacent angles of the parallelogram is 4:5. Remaining three angles of the quadrilateral are in ratio 4 : 11 : 9 respectively. What is the sum of the largest and the smallest angles of the quadrilateral?
A$255^∘ $
B$260^∘$
C$265^∘$
D$270^∘$
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Correct answer is: \(260^∘\)
Explanation:
For the Parallelogram, \(\Large 4x ^{\circ} + 5x ^{\circ} = 180 ^{\circ}\)
\(=> 9x = 180 \implies x = \frac{180}{9} = 20\)
=> smaller angle of parallelogram = \(\Large 4 \times 20 = 80^o\)
Therefore, One angle of the quadrilateral = \(\Large 3 \times 80 = 240^o\)
Now. 4y + 11y + 9y
= 360 - 240 = 120
\(= 24y = 120 \implies y = \frac{120}{24} = 5 \)
=> Its smallest angle
\(= \Large 4 \times 5 = 20^o\)
Therefore, Required sum = \(\Large 240 ^{\circ} + 20 ^{\circ} = 260 ^{\circ}\)
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