Question

in a quadrilateral ABCD, angle a + angle C is 2 times Angle b + Angle d if angle A =140degreeand angleD=60then angle B =​

Answer 1

Answer:

angle a + angle C is 2 times Angle b + Angle d

a=140

d=60

140+angle c=2( angle b+60)

140+angle c=2angle b+120

140-120+angle c=2 angle b

20+angle c=2 angle b

Answer 2

Step-by-step explanation:

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∠ 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)