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The angles of cyclic quadrilaterals ABCD are: A = (6x + 10), B = (5x)°, C = (x + y)° and D = (3y - 10)°. The value of x and y is:
- a)x = 20° and y = 10°
- b)x = 20° and y = 30°
- c)x = 44° and y = 15°
- d)x = 15° and y = 15°
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The angles of cyclic quadrilaterals ABCD are: A = (6x + 10), B = (5x)...
We know, in cyclic quadrilaterals, the sum of the opposite angles are 180°.
Hence,
A + C = 180°
6x + 10 + x + y = 180
=> 7x + y = 170°
And B + D = 180°
5x + 3y - 10 = 180
=> 5x + 3y = 190°
By solving the above two equations we get;
x = 20° and y = 30°.
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The angles of cyclic quadrilaterals ABCD are: A = (6x + 10), B = (5x)...
Given:
- Angles of a cyclic quadrilateral ABCD are: A = (6x + 10)°, B = (5x)°, C = (x + y)°, and D = (3y - 10)°.
To Find:
The values of x and y.
Solution:
A cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. The opposite angles of a cyclic quadrilateral are supplementary, which means they add up to 180°. Using this property, we can find the values of x and y.
Step 1: Angle A and Angle C are Supplementary
Angle A and Angle C are opposite angles in cyclic quadrilateral ABCD. Therefore, they are supplementary.
(6x + 10)° + (x + y)° = 180°
Simplifying the equation, we get:
7x + y = 170 ...(1)
Step 2: Angle B and Angle D are Supplementary
Angle B and Angle D are also opposite angles in cyclic quadrilateral ABCD. Therefore, they are supplementary.
(5x)° + (3y - 10)° = 180°
Simplifying the equation, we get:
5x + 3y = 190 ...(2)
Step 3: Solving the Equations
Now, we have two equations with two variables. We can solve these equations simultaneously to find the values of x and y.
Multiplying equation (1) by 5 and equation (2) by 7, we get:
35x + 5y = 850 ...(3)
35x + 21y = 1330 ...(4)
Subtracting equation (3) from equation (4), we get:
(35x + 21y) - (35x + 5y) = 1330 - 850
16y = 480
Dividing both sides by 16, we get:
y = 30
Substituting the value of y in equation (1), we get:
7x + 30 = 170
7x = 170 - 30
7x = 140
Dividing both sides by 7, we get:
x = 20
Answer:
Therefore, the values of x and y are x = 20° and y = 30°. Hence, option B is the correct answer.
- Angles of a cyclic quadrilateral ABCD are: A = (6x + 10)°, B = (5x)°, C = (x + y)°, and D = (3y - 10)°.
To Find:
The values of x and y.
Solution:
A cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. The opposite angles of a cyclic quadrilateral are supplementary, which means they add up to 180°. Using this property, we can find the values of x and y.
Step 1: Angle A and Angle C are Supplementary
Angle A and Angle C are opposite angles in cyclic quadrilateral ABCD. Therefore, they are supplementary.
(6x + 10)° + (x + y)° = 180°
Simplifying the equation, we get:
7x + y = 170 ...(1)
Step 2: Angle B and Angle D are Supplementary
Angle B and Angle D are also opposite angles in cyclic quadrilateral ABCD. Therefore, they are supplementary.
(5x)° + (3y - 10)° = 180°
Simplifying the equation, we get:
5x + 3y = 190 ...(2)
Step 3: Solving the Equations
Now, we have two equations with two variables. We can solve these equations simultaneously to find the values of x and y.
Multiplying equation (1) by 5 and equation (2) by 7, we get:
35x + 5y = 850 ...(3)
35x + 21y = 1330 ...(4)
Subtracting equation (3) from equation (4), we get:
(35x + 21y) - (35x + 5y) = 1330 - 850
16y = 480
Dividing both sides by 16, we get:
y = 30
Substituting the value of y in equation (1), we get:
7x + 30 = 170
7x = 170 - 30
7x = 140
Dividing both sides by 7, we get:
x = 20
Answer:
Therefore, the values of x and y are x = 20° and y = 30°. Hence, option B is the correct answer.
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The angles of cyclic quadrilaterals ABCD are: A = (6x + 10), B = (5x)°, C = (x + y)° and D = (3y - 10)°. The value of x and y is:a)x = 20° and y = 10°b)x = 20° and y = 30°c)x = 44° and y = 15°d)x = 15° and y = 15°Correct answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The angles of cyclic quadrilaterals ABCD are: A = (6x + 10), B = (5x)°, C = (x + y)° and D = (3y - 10)°. The value of x and y is:a)x = 20° and y = 10°b)x = 20° and y = 30°c)x = 44° and y = 15°d)x = 15° and y = 15°Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angles of cyclic quadrilaterals ABCD are: A = (6x + 10), B = (5x)°, C = (x + y)° and D = (3y - 10)°. The value of x and y is:a)x = 20° and y = 10°b)x = 20° and y = 30°c)x = 44° and y = 15°d)x = 15° and y = 15°Correct answer is option 'B'. Can you explain this answer?.
The angles of cyclic quadrilaterals ABCD are: A = (6x + 10), B = (5x)°, C = (x + y)° and D = (3y - 10)°. The value of x and y is:a)x = 20° and y = 10°b)x = 20° and y = 30°c)x = 44° and y = 15°d)x = 15° and y = 15°Correct answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The angles of cyclic quadrilaterals ABCD are: A = (6x + 10), B = (5x)°, C = (x + y)° and D = (3y - 10)°. The value of x and y is:a)x = 20° and y = 10°b)x = 20° and y = 30°c)x = 44° and y = 15°d)x = 15° and y = 15°Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angles of cyclic quadrilaterals ABCD are: A = (6x + 10), B = (5x)°, C = (x + y)° and D = (3y - 10)°. The value of x and y is:a)x = 20° and y = 10°b)x = 20° and y = 30°c)x = 44° and y = 15°d)x = 15° and y = 15°Correct answer is option 'B'. Can you explain this answer?.
Solutions for The angles of cyclic quadrilaterals ABCD are: A = (6x + 10), B = (5x)°, C = (x + y)° and D = (3y - 10)°. The value of x and y is:a)x = 20° and y = 10°b)x = 20° and y = 30°c)x = 44° and y = 15°d)x = 15° and y = 15°Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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The angles of cyclic quadrilaterals ABCD are: A = (6x + 10), B = (5x)°, C = (x + y)° and D = (3y - 10)°. The value of x and y is:a)x = 20° and y = 10°b)x = 20° and y = 30°c)x = 44° and y = 15°d)x = 15° and y = 15°Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The angles of cyclic quadrilaterals ABCD are: A = (6x + 10), B = (5x)°, C = (x + y)° and D = (3y - 10)°. The value of x and y is:a)x = 20° and y = 10°b)x = 20° and y = 30°c)x = 44° and y = 15°d)x = 15° and y = 15°Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The angles of cyclic quadrilaterals ABCD are: A = (6x + 10), B = (5x)°, C = (x + y)° and D = (3y - 10)°. The value of x and y is:a)x = 20° and y = 10°b)x = 20° and y = 30°c)x = 44° and y = 15°d)x = 15° and y = 15°Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The angles of cyclic quadrilaterals ABCD are: A = (6x + 10), B = (5x)°, C = (x + y)° and D = (3y - 10)°. The value of x and y is:a)x = 20° and y = 10°b)x = 20° and y = 30°c)x = 44° and y = 15°d)x = 15° and y = 15°Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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