Question

In quadrilateral ABCD, side AB is parallel to side DC. If ∠A : ∠D = 1 : 2 and ∠C : ∠B = 4 : 5

(i) Calculate each angle of the quadrilateral.

(ii) Assign a special name to quadrilateral ABCD

Answer 1

(i) ∵ ∠A : ∠D = 1 : 2

Let ∠A = x and ∠D = 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 x 20 = 100°

∠C = 4y = 4 x 20  = 80°

Hence ∠A = 60°; ∠B = 100°; ∠C = 80°

and ∠D = 120°

(ii) `square` ABCD is a trapezium.