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.rhombusb.parallelogramc.trapeziumd.kite

The sum of the angles of a quadrilateral is 360 degrees. If the angles are in the ratio 3:7:6:4, then we can calculate the actual degree measurement of each angle.

First, add up the parts of the ratio: 3 + 7 + 6 + 4 = 20 parts in total.

Then, divide the total degrees in a quadrilateral (360 degrees) by the total parts: 360/20 = 18 degrees per part.

Now, multiply each part of the ratio by 18 to find the degree measurement of each angle:

Angle A = 3 * 18 = 54 degrees Angle B = 7 * 18 = 126 degrees Angle C = 6 * 18 = 108 degrees Angle D = 4 * 18 = 72 degrees

In a parallelogram, opposite angles are equal. Here, Angle A is not equal to Angle C (54 ≠ 108) and Angle B is not equal to Angle D (126 ≠ 72). Therefore, ABCD cannot be a parallelogram.

In a rhombus, all sides are equal, but nothing is mentioned about the sides here. However, we know that in a rhombus, opposite angles are equal, which is not the case here. So, ABCD cannot be a rhombus.

In a trapezium, only one pair of opposite sides is parallel, but nothing is mentioned about the sides here. The angles do not follow any specific rule in a trapezium, so we cannot determine if ABCD is a trapezium based on the given information.

In a kite, two pairs of adjacent sides are equal and one pair of opposite angles (the ones between the unequal sides) are equal. But nothing is mentioned about the sides or specific opposite angles here. So, we cannot determine if ABCD is a kite based on the given information.

Therefore, based on the given information, we cannot definitively classify the quadrilateral ABCD as a rhombus, parallelogram, trapezium, or kite.