Question

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

Options

• parallelogram

• trapezium with PQ || RS

• trapezium with QR || PS

• kite

Answer 1

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.

Explanation:

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

x + 3x + 7x + 9x = 360°   ...[∵ Sum of angles in any quadrilateral is 360°]

⇒ 20x = 360°

⇒ x = `360^circ/20`

⇒ x = 18°

Then, the angles P, Q, R and S are 18°, 54°, 126° and 162°, respectively.

Since, ∠P + ∠S = 18° + 162° = 180° and ∠Q + ∠R = 54° + 126° = 180°

∴ The quadrilateral PQRS is a trapezium with PQ || RS.