Question 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
d) Kite
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∘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∘,
So, PQ∥SR.
∴ The quadrilateral PQRS is a trapezium with PQ∥SR.