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

• rhombus
• kite
• trapezium
• parallelogram

PLEASE HOW THE METHOD BY WHICH YOU GOT YOUR ANSWER

Given, ∠A : ∠B : ∠C : ∠D = 3 : 7 : 6 : 4

Let ∠A = 3x, ∠B = 7x, ∠C = 6x and ∠D = 4x.

In quadrilateral ABCD,

∠A + ∠B + ∠C + ∠D = 360° 

∴ 3x + 7x + 6x + 4x = 360°

⇒ 20x = 360°

⇒ x = 18°

∴ ∠A = 3 × 18° = 546

∠B = 7 × 18° = 126°

∠C = 6 × 18° = 108°

and ∠D = 4 × 18° = 72°

Now, ∠A + ∠B = 54° + 126° = 180°

and ∠C + ∠D = 108° + 72° = 180°

∴ AD || BC               (If a transversal intersect two lines in such a way that a pair of consecutive interior angles are supplementary, then the two lines are parallel)

In the quadrilateral ABCD, the measure of all angles is different and AD || BC.

∴ Quadrilateral ABCD is a trapezium.