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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


A

parallelogram

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B

trapezium with PQ || RS

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C

trapezium with QR||PS

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D

kite

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Solution

The correct option is B

trapezium with PQ || RS


Step 1 - Finding the angles of a quadrilateral

We know that the Sum of all interior angles of quadrilaterals is 360°

Let us assume the angles be x,3x,7x, and 9x

x+3x+7x+9x=36020x=360x=36020x=18

Therefore the angles are

P=x=18°Q=3x=3×18=54°R=7x=7×18=126°S=9x=9×18=162°

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

Step 2 - Finding the sum of opposite angles

P+S=18°+162°=180°Q+R=54°+126°=180°

Therefore, the angle between the pair of parallel sides is supplementary.

So, PQRS is a trapezium with PQRS

Hence, Option B is correct


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