The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral?

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

The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral?

A160°

B 180°

C190°

D 170°

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Correct answer is: 180° Explanation: Sum of the angles of a quadrilateral  = 360 Therefore, $3x+4x+5x+6x=360$ $⟹18x=360$ $⟹x=\frac{360}{18}=20$ Therefore, smallest angle of quadrilateral $=3\times 20=60$  Largest angle of quadrilateral $=6\times 20=120$ Therefore, smallest angle of triangle $=60\times \frac{2}{3}=40$ Largest angle of triangle $=2\times 40=80$ Therefore, third angle of triangle $=180-40-80=60$ Required sum $=60+120=180$ Nithin ? answered Aug 13 '2022 at 21:14 All Comments

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