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Directions: Kindly study the following questions carefully and choose the right answer:
If ABCD be a cyclic quadrilateral in which ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°, then x : y is
- a)3 : 4
- b)4 : 3
- c)5 : 4
- d)4 : 5
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Directions: Kindly study the following questions carefully and choose ...
Understanding Cyclic Quadrilaterals
Cyclic quadrilaterals are quadrilaterals where all vertices lie on a single circle. A key property of cyclic quadrilaterals is that the sum of opposite angles is 180°.
Given Angles
In this problem, we have:
- ∠A = 4x°
- ∠B = 7x°
- ∠C = 5y°
- ∠D = y°
Using the Property of Cyclic Quadrilaterals
According to the property of cyclic quadrilaterals, we know:
∠A + ∠C = 180°
∠B + ∠D = 180°
Substituting the given angles into these equations gives us:
1. From ∠A and ∠C:
4x + 5y = 180 (Equation 1)
2. From ∠B and ∠D:
7x + y = 180 (Equation 2)
Solving the Equations
We can solve these two equations simultaneously.
Step 1: Rearranging Equation 2
From Equation 2:
y = 180 - 7x (Equation 3)
Step 2: Substituting y into Equation 1
Substituting Equation 3 into Equation 1:
4x + 5(180 - 7x) = 180
Expanding this gives:
4x + 900 - 35x = 180
Combining like terms:
-31x + 900 = 180
-31x = 180 - 900
-31x = -720
x = 720 / 31
x = 23.23 (approximately)
Step 3: Finding y
Substituting x back into Equation 3:
y = 180 - 7(23.23)
y ≈ 180 - 162.61
y ≈ 17.39
Finding the Ratio x : y
To find the ratio x : y:
x : y = 23.23 : 17.39
Simplifying this gives approximately:
x : y = 4 : 3
Thus, the correct answer is option B (4 : 3).
Cyclic quadrilaterals are quadrilaterals where all vertices lie on a single circle. A key property of cyclic quadrilaterals is that the sum of opposite angles is 180°.
Given Angles
In this problem, we have:
- ∠A = 4x°
- ∠B = 7x°
- ∠C = 5y°
- ∠D = y°
Using the Property of Cyclic Quadrilaterals
According to the property of cyclic quadrilaterals, we know:
∠A + ∠C = 180°
∠B + ∠D = 180°
Substituting the given angles into these equations gives us:
1. From ∠A and ∠C:
4x + 5y = 180 (Equation 1)
2. From ∠B and ∠D:
7x + y = 180 (Equation 2)
Solving the Equations
We can solve these two equations simultaneously.
Step 1: Rearranging Equation 2
From Equation 2:
y = 180 - 7x (Equation 3)
Step 2: Substituting y into Equation 1
Substituting Equation 3 into Equation 1:
4x + 5(180 - 7x) = 180
Expanding this gives:
4x + 900 - 35x = 180
Combining like terms:
-31x + 900 = 180
-31x = 180 - 900
-31x = -720
x = 720 / 31
x = 23.23 (approximately)
Step 3: Finding y
Substituting x back into Equation 3:
y = 180 - 7(23.23)
y ≈ 180 - 162.61
y ≈ 17.39
Finding the Ratio x : y
To find the ratio x : y:
x : y = 23.23 : 17.39
Simplifying this gives approximately:
x : y = 4 : 3
Thus, the correct answer is option B (4 : 3).
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Community Answer
Directions: Kindly study the following questions carefully and choose ...
The sum of opposite angles of a concyclic quadrilateral is 180°.
∴ ∠A + ∠C = 180°
4x + 5y = 180° ...(i)
∠B + ∠D = 180°
7x + y = 180° ...(ii)
By equation (ii) × 5 – (i), we get
∴ ∠A + ∠C = 180°
4x + 5y = 180° ...(i)
∠B + ∠D = 180°
7x + y = 180° ...(ii)
By equation (ii) × 5 – (i), we get
From equation (ii),
Hence, option B is correct.
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Directions: Kindly study the following questions carefully and choose the right answer:If ABCD be a cyclic quadrilateral in which ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°, then x : y isa)3 : 4b)4 : 3c)5 : 4d)4 : 5Correct answer is option 'B'. Can you explain this answer?
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Directions: Kindly study the following questions carefully and choose the right answer:If ABCD be a cyclic quadrilateral in which ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°, then x : y isa)3 : 4b)4 : 3c)5 : 4d)4 : 5Correct answer is option 'B'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Directions: Kindly study the following questions carefully and choose the right answer:If ABCD be a cyclic quadrilateral in which ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°, then x : y isa)3 : 4b)4 : 3c)5 : 4d)4 : 5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Kindly study the following questions carefully and choose the right answer:If ABCD be a cyclic quadrilateral in which ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°, then x : y isa)3 : 4b)4 : 3c)5 : 4d)4 : 5Correct answer is option 'B'. Can you explain this answer?.
Directions: Kindly study the following questions carefully and choose the right answer:If ABCD be a cyclic quadrilateral in which ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°, then x : y isa)3 : 4b)4 : 3c)5 : 4d)4 : 5Correct answer is option 'B'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Directions: Kindly study the following questions carefully and choose the right answer:If ABCD be a cyclic quadrilateral in which ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°, then x : y isa)3 : 4b)4 : 3c)5 : 4d)4 : 5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Kindly study the following questions carefully and choose the right answer:If ABCD be a cyclic quadrilateral in which ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°, then x : y isa)3 : 4b)4 : 3c)5 : 4d)4 : 5Correct answer is option 'B'. Can you explain this answer?.
Solutions for Directions: Kindly study the following questions carefully and choose the right answer:If ABCD be a cyclic quadrilateral in which ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°, then x : y isa)3 : 4b)4 : 3c)5 : 4d)4 : 5Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC CGL.
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Directions: Kindly study the following questions carefully and choose the right answer:If ABCD be a cyclic quadrilateral in which ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°, then x : y isa)3 : 4b)4 : 3c)5 : 4d)4 : 5Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Directions: Kindly study the following questions carefully and choose the right answer:If ABCD be a cyclic quadrilateral in which ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°, then x : y isa)3 : 4b)4 : 3c)5 : 4d)4 : 5Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Directions: Kindly study the following questions carefully and choose the right answer:If ABCD be a cyclic quadrilateral in which ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°, then x : y isa)3 : 4b)4 : 3c)5 : 4d)4 : 5Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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