Question

ABCD is a trapezium such that AB || CD, ∠A : ∠D = 2 : 1, ∠B : ∠C = 7 : 5. Find the angles of the trapezium.

Answer 1

Given that ABCD is a trapezium such that AB || CD

Let ∠A = 2x, ∠D = x, ∠B = 7y, ∠C = 5y

Since, AB || CD and AD is a transversal

∴ ∠A + ∠D = 180°   ...(Co-interior angles)

`\implies` 2x + x = 180°

`\implies` 3x = 180°

`\implies x = 180^circ/3 = 60^circ`

∴ ∠A = 2x = 2 × 60° = 120° and ∠D = 60°

Again, AB || CD and BC is a transversal.

∴ ∠B + ∠C = 180°   ...(Co-interior angles)

`\implies` 7y + 5y = 180°

`\implies` 12y = 180°

`\implies y = 180^circ/12 = 15^circ`

∴ ∠B = 7y = 7 × 15° = 105° and ∠C = 5y = 5 × 15° = 75°

Hence, ∠A = 120°, ∠B = 105°, ∠C = 75° and ∠D = 60°