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 ∠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^o

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