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

Question

In a quadrilateral ABCD, &#x2220; A+ &#x2220; C is 2 times &#x2220; B+ &#x2220; D. If &#x2220; A= 140&#xB0; and f &#x2220; D = 60&#xB0;, then &#x2220; B=

Philoid · Accepted Answer

Given that,

∠A = 140°

∠D = 60°

According to question,

∠A + ∠C = 2 (∠B + ∠D)

140 + ∠C = 2 (∠B + 60°)

∠B = (∠C) + 10° (i)

We know,

∠A + ∠B + ∠C + ∠D= 360°

140° + (∠C) + 10° + ∠C + 60° = 360°

∠C = 150°

∠C = 100°

∠B = (100°) + 10°

= 60°

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