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

Let ABCD is a trapezium and AB || CD.

Also, angles A and D be 2x and x respectively.

So, 2x + x = 180°  ...[In trapezium, the angles on either side of the base are supplementary]

⇒ 3x = 180°

⇒ x = 60°

So, ∠A = 2 × 60° = 120°

And ∠D = 60°

Again, let the angles B and C be 7x and 5x respectively.

So, 7x + 5x = 180°

⇒ 12x = 180°

⇒ x = 15°

Hence, ∠B = 7 × 15 = 105° and ∠C = 5 × 15 = 75°.