Question

in a quadrilateral ABCD angle A + angle C is two times Angle B + angle D. If angle A = to 140 degree and Angle D = 60 degree, then Angle B equal to ???​

Answer 1

Step-by-step explanation:

• use the concepts carefully mentioned in the answer
• sum of angles of quadrilateral is always 360 degrees

Answer 2

Answer:

∠B = 60°

Step-by-step explanation:

In quadrilateral ABCD

⇒ ∠A + ∠C = 2(∠B + ∠D)

⇒ ∠A + ∠C = 2∠B + 2∠D

Adding 2∠A + 2∠C both sides

2∠A + 2∠C + ∠A + ∠C = 2∠A + 2∠B + 2∠C + 2∠D

⇒ 3∠A + 3∠C = 2(∠A + ∠B + ∠C + ∠D)

⇒ 3(∠A + ∠C) = 2 x 360° = 720°

∴ ∠A + ∠C = 720° /3  = 240°

⇒ 40° + ∠C = 240° (∵ ∠A = 40°)

∠C = 240° – 40° = 200°

Now 2(∠B + ∠D) = ∠A + ∠C = 240°

∠B + ∠D = 240° /2  = 120°

∴ ∠B = 60° = 120°

∴ ∠B = 60°