Question

The angles of a quadrilateral ABCD taken in an order are in the ratio 3 : 7 : 6 : 4. Then
ABCD is a
(a) kite (b) parallelogram (c) rhombus (d) trapezium

Answer 1

D) Since all sides measure different, the answer will be trapezium

Answer 2

Given : Ratios of angles of quadrilateral are 3:4:6:5

Now,

Let the angles of quadrilateral be 3x, 7x, 6x and 4x.

We know that,

The sum of the angle of a quadrilateral = 360°

3x + 7x + 6x + 4x = 360°

20x = 360°

x = 360°/20

x = 18°

Now,

The angles are,

⇒ ∠A=3x=54°

⇒ ∠B=7x=126°

⇒ ∠C=6x=108°

⇒∠D=4x=72°

⇒∠BCE=∠ADC=72°

Since the corresponding angles are equal, i.e BC∥AD

∴ Sum of interior angles

⇒∠A+∠B=126°+54°=180°

⇒∠C+∠D=108°+72°=180°

∴ ABCD is a trapezium.

Hence, the answer is trapezium.

Look at attachment for diagram

Hope you understand