Question

In a quadrilateral ABCD, Side AB is parallel to DC. If angle A : angle D= 1:2 and angle C : angle B = 4:5 Calculate each angle of the quadrilateral. pls answer this question properly and quickly... pls​

Answer 1

Answer:

∠A : ∠D = 1:2 Let ∠A = x and ∠B = 2x ∵ ∠C : ∠B = 4 : 5 Let ∠C = 4y and ∠B = 5y ∵ AB || DC ∠A + ∠D = 180° x + 2x = 180° 3x = 180° x = 60° ∴ A = 60° ∠D = 2x = 2 x 60 = 120° Again ∠B + ∠C = 180° 5y + 4y= 180° 9y = 180° y = 20° ∴ ∠B = 5y = 5 x 20 = 100° ∠C = 4y = 4 x 20 = 80° Hence ∠A = 60° ; ∠B = 100° ; ∠C = 80° and ∠D = 120 degree

Hope it helps you keep smiling :)

Answer 2

∠A : ∠D = 1 : 2

Let ∠A = x and ∠B = 2x

∵ ∠C : ∠B = 4 : 5

Let ∠C = 4y and ∠B = 5y

∵ AB ∥ DC

∴ ∠A + ∠D = 180°

x + 2x = 180°

3x = 180°

x = 60°

∴ A = 60°

∠D = 2x = 2 × 60 = 120°

Again ∠B + ∠C = 180°

5y + 4y = 180°

9y = 180°

y = 20°

∴ ∠B = 5y = 5 × 20 = 100°

∠C = 4Y = 4 × 20 = 80°

Hence ∠A = 60°; ∠B = 100° ; ∠C = 80°

and ∠D = 120°

(ii) Quadrilateral ABCD is a trapezium because one pair of opposite side is parallel.