Class 9 Exam > Class 9 Questions > 1) If the angles of a quadrilateral are in ra...
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1) If the angles of a quadrilateral are in ratio 4:3,4:7.Find the largest angle of the quadrilateral. 2) Length of each side of a rhombus PQRS is 15cm.Diagonal PR=24cm.Find the length of diagonal QS. 3) In the trapezium PQRS,PQ parallel to RS and angleP=60degree.find the measure of angle S?
Verified Answer
1) If the angles of a quadrilateral are in ratio 4:3,4:7.Find the larg...
Since the angle of a quadrilateral are in ratio of 4:3:4:7.
So suppose the angles of quadrilateral are 4x, 3x, 4x, and 7x.
We know that sum of the angles of quadrilateral is 360 degree. So we have;
Therefore the largest angle of quadrilateral is 140 degree.
This question is part of UPSC exam. View all Class 9 courses
Most Upvoted Answer
1) If the angles of a quadrilateral are in ratio 4:3,4:7.Find the larg...
Answer of first question
Let the angles of
quadrilateral be 4x,3x,4x,7x
Sum of all angles of quadrilateral=360degree
4x+3x+4x+7x=360degree
=>18x=360
=>x=20degree
Angles of quadrilateral
4x=4×20=80degree
3x=3×20=60degree
4x=4×20=80degree
7x=7×20=140degree
(80,60,80,140degree)
largest angle=140degree(Ans).
Let the angles of
quadrilateral be 4x,3x,4x,7x
Sum of all angles of quadrilateral=360degree
4x+3x+4x+7x=360degree
=>18x=360
=>x=20degree
Angles of quadrilateral
4x=4×20=80degree
3x=3×20=60degree
4x=4×20=80degree
7x=7×20=140degree
(80,60,80,140degree)
largest angle=140degree(Ans).
Community Answer
1) If the angles of a quadrilateral are in ratio 4:3,4:7.Find the larg...
1) Finding the largest angle of a quadrilateral:
To find the largest angle of a quadrilateral, we need to know the angles of the quadrilateral. Let's consider the given ratios:
Angle A : Angle B = 4:3
Angle C : Angle D = 4:7
Let's assign variables to these angles:
Angle A = 4x
Angle B = 3x
Angle C = 4y
Angle D = 7y
The sum of the angles in a quadrilateral is always 360 degrees. Therefore, we can write the equation:
4x + 3x + 4y + 7y = 360
Combining like terms, we get:
7x + 11y = 360
To find the largest angle, we need to maximize either x or y. Let's maximize x by assuming y = 0.
7x + 11(0) = 360
7x = 360
x = 360/7
Now, we can find the largest angle:
Angle D = 7y = 7(0) = 0
Therefore, the largest angle of the quadrilateral is 0 degrees.
2) Finding the length of diagonal QS in a rhombus:
In a rhombus, the diagonals are perpendicular bisectors of each other. Therefore, we can use the Pythagorean theorem to find the length of diagonal QS.
Let's consider the given information:
Length of each side of the rhombus = 15 cm
Diagonal PR = 24 cm
Let's assume the length of diagonal QS is d cm.
Using the Pythagorean theorem in triangle PQS, we can write:
(1/2 * 15)^2 + (1/2 * d)^2 = 24^2
Simplifying the equation:
225 + (d/2)^2 = 576
(d/2)^2 = 576 - 225
(d/2)^2 = 351
d/2 = √351
d = 2 * √351
Therefore, the length of diagonal QS in the rhombus is 2 times the square root of 351 cm.
3) Finding the measure of angle S in a trapezium:
In a trapezium, the opposite angles are supplementary. Therefore, we can find the measure of angle S by subtracting the measure of angle P from 180 degrees.
Given information:
Angle P = 60 degrees
To find angle S, we use the equation:
Angle S = 180 - Angle P
Substituting the given value:
Angle S = 180 - 60
Angle S = 120 degrees
Therefore, the measure of angle S in the trapezium is 120 degrees.
To find the largest angle of a quadrilateral, we need to know the angles of the quadrilateral. Let's consider the given ratios:
Angle A : Angle B = 4:3
Angle C : Angle D = 4:7
Let's assign variables to these angles:
Angle A = 4x
Angle B = 3x
Angle C = 4y
Angle D = 7y
The sum of the angles in a quadrilateral is always 360 degrees. Therefore, we can write the equation:
4x + 3x + 4y + 7y = 360
Combining like terms, we get:
7x + 11y = 360
To find the largest angle, we need to maximize either x or y. Let's maximize x by assuming y = 0.
7x + 11(0) = 360
7x = 360
x = 360/7
Now, we can find the largest angle:
Angle D = 7y = 7(0) = 0
Therefore, the largest angle of the quadrilateral is 0 degrees.
2) Finding the length of diagonal QS in a rhombus:
In a rhombus, the diagonals are perpendicular bisectors of each other. Therefore, we can use the Pythagorean theorem to find the length of diagonal QS.
Let's consider the given information:
Length of each side of the rhombus = 15 cm
Diagonal PR = 24 cm
Let's assume the length of diagonal QS is d cm.
Using the Pythagorean theorem in triangle PQS, we can write:
(1/2 * 15)^2 + (1/2 * d)^2 = 24^2
Simplifying the equation:
225 + (d/2)^2 = 576
(d/2)^2 = 576 - 225
(d/2)^2 = 351
d/2 = √351
d = 2 * √351
Therefore, the length of diagonal QS in the rhombus is 2 times the square root of 351 cm.
3) Finding the measure of angle S in a trapezium:
In a trapezium, the opposite angles are supplementary. Therefore, we can find the measure of angle S by subtracting the measure of angle P from 180 degrees.
Given information:
Angle P = 60 degrees
To find angle S, we use the equation:
Angle S = 180 - Angle P
Substituting the given value:
Angle S = 180 - 60
Angle S = 120 degrees
Therefore, the measure of angle S in the trapezium is 120 degrees.
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1) If the angles of a quadrilateral are in ratio 4:3,4:7.Find the largest angle of the quadrilateral. 2) Length of each side of a rhombus PQRS is 15cm.Diagonal PR=24cm.Find the length of diagonal QS. 3) In the trapezium PQRS,PQ parallel to RS and angleP=60degree.find the measure of angle S?
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1) If the angles of a quadrilateral are in ratio 4:3,4:7.Find the largest angle of the quadrilateral. 2) Length of each side of a rhombus PQRS is 15cm.Diagonal PR=24cm.Find the length of diagonal QS. 3) In the trapezium PQRS,PQ parallel to RS and angleP=60degree.find the measure of angle S? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about 1) If the angles of a quadrilateral are in ratio 4:3,4:7.Find the largest angle of the quadrilateral. 2) Length of each side of a rhombus PQRS is 15cm.Diagonal PR=24cm.Find the length of diagonal QS. 3) In the trapezium PQRS,PQ parallel to RS and angleP=60degree.find the measure of angle S? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1) If the angles of a quadrilateral are in ratio 4:3,4:7.Find the largest angle of the quadrilateral. 2) Length of each side of a rhombus PQRS is 15cm.Diagonal PR=24cm.Find the length of diagonal QS. 3) In the trapezium PQRS,PQ parallel to RS and angleP=60degree.find the measure of angle S?.
1) If the angles of a quadrilateral are in ratio 4:3,4:7.Find the largest angle of the quadrilateral. 2) Length of each side of a rhombus PQRS is 15cm.Diagonal PR=24cm.Find the length of diagonal QS. 3) In the trapezium PQRS,PQ parallel to RS and angleP=60degree.find the measure of angle S? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about 1) If the angles of a quadrilateral are in ratio 4:3,4:7.Find the largest angle of the quadrilateral. 2) Length of each side of a rhombus PQRS is 15cm.Diagonal PR=24cm.Find the length of diagonal QS. 3) In the trapezium PQRS,PQ parallel to RS and angleP=60degree.find the measure of angle S? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1) If the angles of a quadrilateral are in ratio 4:3,4:7.Find the largest angle of the quadrilateral. 2) Length of each side of a rhombus PQRS is 15cm.Diagonal PR=24cm.Find the length of diagonal QS. 3) In the trapezium PQRS,PQ parallel to RS and angleP=60degree.find the measure of angle S?.
Solutions for 1) If the angles of a quadrilateral are in ratio 4:3,4:7.Find the largest angle of the quadrilateral. 2) Length of each side of a rhombus PQRS is 15cm.Diagonal PR=24cm.Find the length of diagonal QS. 3) In the trapezium PQRS,PQ parallel to RS and angleP=60degree.find the measure of angle S? in English & in Hindi are available as part of our courses for Class 9.
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1) If the angles of a quadrilateral are in ratio 4:3,4:7.Find the largest angle of the quadrilateral. 2) Length of each side of a rhombus PQRS is 15cm.Diagonal PR=24cm.Find the length of diagonal QS. 3) In the trapezium PQRS,PQ parallel to RS and angleP=60degree.find the measure of angle S?, a detailed solution for 1) If the angles of a quadrilateral are in ratio 4:3,4:7.Find the largest angle of the quadrilateral. 2) Length of each side of a rhombus PQRS is 15cm.Diagonal PR=24cm.Find the length of diagonal QS. 3) In the trapezium PQRS,PQ parallel to RS and angleP=60degree.find the measure of angle S? has been provided alongside types of 1) If the angles of a quadrilateral are in ratio 4:3,4:7.Find the largest angle of the quadrilateral. 2) Length of each side of a rhombus PQRS is 15cm.Diagonal PR=24cm.Find the length of diagonal QS. 3) In the trapezium PQRS,PQ parallel to RS and angleP=60degree.find the measure of angle S? theory, EduRev gives you an
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