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In a quadrilateral ABCD, ∠A+∠C is 2 times ∠B+∠D. If ∠A = 140° and ∠D = 60°, then ∠B = 

A. 60° 

B. 80° 

C. 120° 

D. none of these

1 Answer

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Best answer

Option : (A)

Given, 

ABCD is a parallelogram 

∠A+∠C = 2(∠B+∠D) 

∠A = 40° 

∵ ∠A+∠B+∠C+∠D = 360° 

[angle sum property of quadrilateral] 

= ∠A+∠C+∠B+∠D = 360° 

= 2(∠B+∠D)+ ∠B+∠D = 360° 

= 3(∠B+∠D) = 360°

= ∠B+∠D = \(\frac{360°}{3}\) = 120°

∵∠D = 60° [given] 

∴ ∠B = 120°- 60° = 60°

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