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The angles P, Q, R and S of a quadrilateral are in the ratio 1:3:7:9. Then PQRS is a
(a) parallelogram
(b) trapezium with PQ || RS
(c) trapezium with QR||PS
(d) kite

Solution:

Given, the angles P, Q, R and S of a quadrilateral are in the ratio 1:3:7:9.

We have to find the type of quadrilateral PQRS.

We know that the sum of the angles of a quadrilateral is equal to 360 degrees.

Let the angles be x, 3x, 7x and 9x.

So, x + 3x + 7x + 9x = 360°

20x = 360°

x = 360°/20

x = 18°

Now, 3x = 3(18°) = 54°

7x = 7(18°) = 126°

9x = 9(18°) = 162°

The angles of the quadrilateral PQRS are 18°, 54°, 126° and 162°.

∠P + ∠S = 18° + 162° = 180°

∠Q + ∠R = 54° + 126° = 180°

This implies that the angle between the pair of parallel sides is supplementary.

Therefore, PQRS is a trapezium with PQ || RS

✦ Try This: The angles A, B, C and D of a quadrilateral are in the ratio 1:2:5:7. Find the angles.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 47

The angles P, Q, R and S of a quadrilateral are in the ratio 1:3:7:9. Then PQRS is a (a) parallelogram (b) trapezium with PQ || RS (c) trapezium with QR||PS

Summary:

The angles P, Q, R and S of a quadrilateral are in the ratio 1:3:7:9. Then PQRS is a trapezium with PQ || RS.

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