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If angles P, Q, R and S of the quadrilateral PQRS, taken in order, are in the ratio 3:7:6:4, what is PQRS?
- a)A rhombus
- b)A parallelogram
- c)A trapezium
- d)A kite
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If angles P, Q, R and S of the quadrilateral PQRS, taken in order, are...
Let the angles be 3x, 7x , 6x and 4x.
∴ 3x+7x+6x+4x = 360o or 20x = 360o or x = 18o.
The angles are 54o,126o,108o and 72o.
We see that adjacent angles are supplementary but opposite angles-are not equal. Clearly, it is a trapezium.
∴ 3x+7x+6x+4x = 360o or 20x = 360o or x = 18o.
The angles are 54o,126o,108o and 72o.
We see that adjacent angles are supplementary but opposite angles-are not equal. Clearly, it is a trapezium.
Most Upvoted Answer
If angles P, Q, R and S of the quadrilateral PQRS, taken in order, are...
Understanding the Problem:
In the given question, angles P, Q, R, and S of the quadrilateral PQRS are in the ratio 3:7:6:4 respectively.
Identifying the Type of Quadrilateral:
To determine the type of quadrilateral PQRS, we need to analyze the given angle ratios.
Angle Sum Property of a Quadrilateral:
The sum of all angles in a quadrilateral is always 360 degrees.
Calculating the Angles:
Let the common ratio be x.
Therefore, the angles of the quadrilateral are 3x, 7x, 6x, and 4x respectively.
According to the angle sum property,
3x + 7x + 6x + 4x = 360
20x = 360
x = 18
Therefore, angles are 3(18), 7(18), 6(18), and 4(18) which are 54, 126, 108, and 72 degrees respectively.
Identifying the Type:
Now, we need to check if these angles form a trapezium.
In a trapezium, one pair of opposite angles should be equal and the other pair should be supplementary.
Checking the angles, we find that the sum of opposite angles (126° and 54°) is 180° which satisfies the trapezium condition.
Therefore, the quadrilateral PQRS is a trapezium.
In the given question, angles P, Q, R, and S of the quadrilateral PQRS are in the ratio 3:7:6:4 respectively.
Identifying the Type of Quadrilateral:
To determine the type of quadrilateral PQRS, we need to analyze the given angle ratios.
Angle Sum Property of a Quadrilateral:
The sum of all angles in a quadrilateral is always 360 degrees.
Calculating the Angles:
Let the common ratio be x.
Therefore, the angles of the quadrilateral are 3x, 7x, 6x, and 4x respectively.
According to the angle sum property,
3x + 7x + 6x + 4x = 360
20x = 360
x = 18
Therefore, angles are 3(18), 7(18), 6(18), and 4(18) which are 54, 126, 108, and 72 degrees respectively.
Identifying the Type:
Now, we need to check if these angles form a trapezium.
In a trapezium, one pair of opposite angles should be equal and the other pair should be supplementary.
Checking the angles, we find that the sum of opposite angles (126° and 54°) is 180° which satisfies the trapezium condition.
Therefore, the quadrilateral PQRS is a trapezium.
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If angles P, Q, R and S of the quadrilateral PQRS, taken in order, are in the ratio3:7:6:4, what is PQRS?a)A rhombusb)A parallelogramc)A trapeziumd)A kiteCorrect answer is option 'C'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about If angles P, Q, R and S of the quadrilateral PQRS, taken in order, are in the ratio3:7:6:4, what is PQRS?a)A rhombusb)A parallelogramc)A trapeziumd)A kiteCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If angles P, Q, R and S of the quadrilateral PQRS, taken in order, are in the ratio3:7:6:4, what is PQRS?a)A rhombusb)A parallelogramc)A trapeziumd)A kiteCorrect answer is option 'C'. Can you explain this answer?.
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