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?

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BANK PO Exam (UCO Bank) 2011 click here to view all questions

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: ${260}^{\circ }$ Explanation:   For the Parallelogram,  $4x^{\circ }+5x^{\circ }={180}^{\circ }$ $=>9x=180⟹x=\frac{180}{9}=20$ => smaller angle of parallelogram = $4\times 20={80}^o$ Therefore, One angle of the quadrilateral = $3\times 80={240}^o$ Now. 4y + 11y + 9y = 360 - 240 = 120 $=24y=120⟹y=\frac{120}{24}=5$ => Its smallest angle $=4\times 5={20}^o$ Therefore, Required sum = ${240}^{\circ }+{20}^{\circ }={260}^{\circ }$ Nithin ? answered Aug 13 '2022 at 20:53 All Comments

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