In a quadrilateral ABCD, ∠A + ∠C is two times ∠B and ∠D. If ∠A = 140˚ and ∠D = 60˚, the find ∠B.

To Find: ∠B

Given: ∠A + ∠C = 2(∠B and ∠D), ∠D = 60˚, and ∠A = 140˚

Concept Used:

Sum of area of a quadrilateral = 360˚

Explanation:

∠A + ∠B + ∠C + ∠D = 360˚

Now, putting, ∠A + ∠C = 2(∠B and ∠D) we get,

∠A + ∠C + 1/2 (∠A + ∠C) = 360˚

Putting the value of ∠A, we get,

420˚ + 3 ∠C = 720˚

3∠C = 300˚

∠C = 100˚

Now,

∠A + ∠C = 2(∠B + ∠D)

140˚ + 100˚ = 2(∠B + 60˚)

2(∠B + 60˚) = 240˚

∠B + 60˚ = 120˚

∠B = 60˚

Hence, ∠B = 60˚.