Question

The angles A, B, C and D of a trapezium ABCD are in the ratio 3: 4: 5: 6. Le. ∠A : ∠B : ∠C : ∠D = 3:4: 5 : 6. Find all the angles of the trapezium. Also, name the two sides of this trapezium which are parallel to each other. Give reason for your answer.

Answer 1

As the trapezium ABCD is a quadrilateral,

∴ Sum of its interior angles = 360°

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ 3x + 4x + 5x + 6x = 360°

⇒ 18x = 360°

⇒ x = `360^circ/18 = 20°`

∴ ∠A = 3x = 3 × 20° = 60°

and ∠B = 4x = 4 × 20° = 80°

and ∠C = 5x = 5 × 20° = 100°

and ∠D = 6x = 6 × 20° = 120°

AB is parallel to DC.

∵ ∠A + ∠D = 180°

∠A and ∠D are co-interior angles whose sum = 180°