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

a) Calculate each angle of the quadrilateral.

b) Assign a special name to quadrilateral ABCD.

Given: ∠A : ∠D = 1 : 2 and ∠C : ∠B = 4 : 5

To find: ∠ A, ∠B, ∠C, ∠D

∠D = 180° – ∠A …….(1)

[AB and CD are parallel and the sum of angles made on straight line = 180°]

∠C = 180° – ∠B ….(2)

[AB and CD are parallel and the sum of angles made on straight line = 180°]

Let ∠A =x then ∠D = 2x

From eq(1) we get,

2x = 180° –x

3x = 180°

x = 60°

Let ∠C = 4y

And ∠B = 5y

From eq(2) we get,

4y = 180° – 5y

9y = 180°

y = 20°

a) So we have the angles of the quadrilateral as follows:

∠A =x = 60°

∠B = 5y = 5 × 20° = 100°

∠C = 4y = 4 × 20° = 80°

∠D = 2x = 2 × 60° = 120°

b) As two of the sides of a quadrilateral are parallel. The quadrilateral is a Trapezium.