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 ___________.

 As angles A, B, C, and D of the quadrilateral ABCD, taken in order, are in the ratio 3: 7: 6: 4,

We have the angles A, B, C and D = 3x, 7x, 6x, and 4x.

Now, the sum of the angle of a quadrilateral = 360^o.

⇒ 3x + 7x + 6x + 4x = 360^o

⇒ 20x = 360^o

⇒ x = 360 ÷ 20 =18^o

So, the angles A, B, C and D of quadrilateral ABCD are,

∠A = 3×18^o = 54^o,

∠B = 7×18^o = 126^o

∠C = 6×18^o = 108^o

∠D = 4×18^o = 72^o

AD and BC are two lines cut by a transversal CD

Now, the sum of angles ∠C and ∠D on the same side of the transversal,

⇒ ∠C + ∠D = 108^o + 72^o = 180^o

Hence, AD|| BC.

So, ABCD is a quadrilateral in which one pair of opposite sides are parallel.

Hence, ABCD is a trapezium.