Multiple Choice Question (MCQ)
The angles of a quadrilateral ABCD taken in an order are in the ratio 3 : 7 : 6 : 4. Then ABCD is a

×
kite

×
parallelogram

×
rhombus

✓
trapezium
The angles of a quadrilateral ABCD taken in an order are in the ratio 3 : 7 : 6 : 4. Then ABCD is a
kite
parallelogram
rhombus
trapezium
Given, the angles of a quadrilateral ABCD taken in an order are in the ratio 3:7:6:4
We have to find the type of the quadrilateral.
Let the angles of the quadrilateral ABCD be 3x, 7x, 6x and 4x.
We know that the sum of all angles of a quadrilateral is equal to 360 degrees.
Therefore
3x + 7x + 6x + 4x = 360°
20x = 360°
x = \dfrac{360°}{20}
x = 18°
Now four interior angles are calculated below
A = 3x = 3\cdot 18° = 54°
B = 7x = 7\cdot 18° = 126°
C = 6x = 6\cdot 18° = 108°
D = 4x = 4\cdot 18° = 72°
AD and BC are two lines cut by a transversal CD.
Now, sum of angles C and D on the same side of transversal,
C + D =108° + 72° =180°
This is the same for angle A and B
A + B =54° + 126° =180°
We know that the sum of interior angles on the same side of the transversal is equal to 180 \degree , then the two lines are parallel.
therefoer, AD BC
This implies ABCD is a quadrilateral in which one pair of opposite sides are parallel.
Therefore, ABCD is a trapezium.