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

Solution:

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.

So, 3x + 7x + 6x + 4x = 360°

10x + 10x = 360°

20x = 360°

x = 360°/20

x = 18°

Now, A = 3x = 3(18) = 54°

B = 7x = 7(18) = 126°

C = 6x = 6(18) = 108°

D = 4x = 4(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°

We know that the sum of interior angles on the same side of the transversal is equal to 180 degrees, then the two lines are parallel.

So, AD|| BC

This implies ABCD is a quadrilateral in which one pair of opposite sides are parallel.

Therefore, ABCD is a trapezium.

✦ Try This: The angles of a quadrilateral PQRS taken in an order are in the ratio 2:3:4:5. Then ABCD is a

(a) kite

(b) parallelogram

(c) rhombus

(d) none of these

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Solved Problem 2

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

Summary:

The angles of a quadrilateral ABCD taken in an order are in the ratio 3:7:6:4. Then ABCD is a trapezium.

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