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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
Solution
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.
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