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If $∠ P, ∠ Q, ∠ R and ∠ S$ of a quadrilateral PQRS are in the ratio 3: 7: 6: 4 when taken in order, PQRS is a

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Kite

Rhombus

Trapezium

Parallelogram

answer is C.

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Detailed Solution

Given the angles are in the ratio 3:7:6:4 of a quadrilateral PQRS.
Question Image

Let the required angles be 3x, 7x, 6x, and 4x.
It is known that sum of the angles of the quadrilateral is

360 °

.
Therefore,

3 x + 7 x + 6 x + 4 x = 360 ° 20 x = 360 ° x = 18 °

From the value of x we get,
3x = 54,
4x = 72,
6x = 108,
7x = 126.
We can see that,

54 ° + 126 ° = 180 °

and

72 ° + 108 ° = 180 °

.
This implies that the sum of angles which is between two parallel lines is supplementary.
This is the property of trapezium.
Thus, PQRS is a trapezium.
Hence, option 3 is the correct choice.

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