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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 PQRS
c) Trapezium with QRPS
d) Kite

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Solution


Let the angles be x, 3x, 7x and 9x, then,
x+3x+7x+9x=360 [ sum of angles in any quadrilateral is 360]
20x=360x=36020x=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, PQSR.
The quadrilateral PQRS is a trapezium with PQSR.


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