Question

in a quadrilateral ABCD. angle A+angle C is 2 times angle B+angle D, if angle A is 140 degree, and angle d is 60 degree then angle b =

Answer 1

just put the values, you will get the answer

Answer 2

∠ B = 60°

Step-by-step explanation:

In a quadrilateral ABCD, given that ∠ A + ∠ C = 2( ∠ B + ∠ D) ........ (1)

Now, for a quadrilateral, ∠ A + ∠ B + ∠ C + ∠ D = 360°

⇒ 2(∠ B + ∠ D) + (∠ B + ∠ D) = 360° {From equation (1)}

⇒ 3(∠ B + ∠ D) = 360°

⇒ ∠ B + ∠ D = 120°  .......... (2)

⇒ ∠ A + ∠ C = 2 × 120° = 240°  {From equation (1)}............ (3)

Now, given that ∠ D = 60°

So, from equation (2) we get, ∠ B = 120° - ∠ D = 120° - 60° = 60° (Answer)