Question

Ian quadrilateral abcd angle a +angle d is twice angle c+angle d. Of angle a is 140 and angle d is 60 find angle b

Answer 1

Ratio of angle B and angle D = 1 : 3

Let angle B = x and angle D = 3x

Ratio of angle A and angle C = 5 : 6

Let angle A = 5x and angle C = 6x

But Angle B + angle D = 140°

x + 3x = 140°

4x = 140°

x = 35°

Angle B = x = 1 × 35 = 35°

Angle D = 3x = 3 × 35 = 105°

As the sum of B and D is 140 degrees....therefore, the sum of angles A and C is equal to 220 degrees

5x + 6x = 220  ⇒  x = 20°

angle A = 5×20 = 100 °

angle C = 6 × 20 = 120°