Question

If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3 : 7 : 6 : 4, then ABCD is a _________.

Answer 1

Let the angle A, B, C and D of a quadrilateral be 3x, 7x, 6x and 4x, respectively.

We have,
Sum of all the angles of a quadrilateral = 360°
⇒ 3x + 7x + 6x + 4x = 360°
⇒ 20x = 360°
​⇒ x = 18°

Thus, ∠A = 54°
∠B = 126°
∠C = 108°
∠D = 72°



Now,
∠BCE = 180° − 108° = 72° = ∠ADE
⇒ AD || BC

Hence, ABCD is a trapezium.