Question

The following figure shows a quadrilateral in which sides AB and DC are parallel. If ∠A : ∠D = 4 : 5, ∠B = (3x – 15)° and ∠C = (4x + 20)°, find each angle of the quadrilateral ABCD.

Answer 1

Let ∠A = 4x

∠D = 5x

Since ∠A + ∠D = 180° [AB||DC]

4x + 5x = 180°

⇒ 9x = 180°

⇒ x = 20°

∠A = 4 (20) = 80°,

∠D = 5 (20) = 100°

Again ∠B + ∠C = 180° [ AB||DC]

3x – 15° + 4x + 20° = 180°

7x = 180° – 5°

⇒ 7x = 175°

⇒ x = 25°

∠B = 75° – 15° = 60°

and ∠C = 4 (25) + 20 = 100°+ 20°= 120°