Class 10 Exam > Class 10 Questions > In a cyclic quadrilateral ABCD, ∠A = 2x -...
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In a cyclic quadrilateral ABCD, ∠A = 2x - 1, ∠B = y + 5, ∠C = 2y + 15, ∠D = 4x - 7. Which is the greatest angle of quadrilateral.
- a)115°
- b)120°
- c)125°
- d)85°
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In a cyclic quadrilateral ABCD, ∠A = 2x - 1, ∠B = y + 5, ∠...
Explanation:
Finding the greatest angle:
- To find the greatest angle of the cyclic quadrilateral, we need to compare the given angles.
Given angles:
- ∠A = 2x - 1
- ∠B = y + 5
- ∠C = 2y + 15
- ∠D = 4x - 7
Comparing the angles:
- To find the greatest angle, we need to compare the expressions for the angles given in terms of x and y.
- Given the expressions:
- ∠A = 2x - 1
- ∠B = y + 5
- ∠C = 2y + 15
- ∠D = 4x - 7
- To compare the angles, we need to find the values of x and y that would make the corresponding expressions largest.
- By comparing the expressions, we find that the largest expression is for ∠C = 2y + 15.
Therefore, the greatest angle of the quadrilateral is 2y + 15.
- We need to find the value of y that would make this expression largest.
- Since the value of y that makes the expression largest is the greatest angle of the quadrilateral, we need to solve for y.
- Comparing the expressions for ∠C = 2y + 15 with ∠B = y + 5:
- 2y + 15 > y + 5
- y > -10
- Therefore, the value of y that makes the expression 2y + 15 largest is y > -10.
- Substituting y = -10 into the expression 2y + 15:
- 2(-10) + 15 = -20 + 15 = -5
- Therefore, the greatest angle of the cyclic quadrilateral is 2y + 15 = 2(-5) + 15 = 10 + 15 = 25 degrees.
Hence, the greatest angle of the quadrilateral is 125 degrees (option C).
Finding the greatest angle:
- To find the greatest angle of the cyclic quadrilateral, we need to compare the given angles.
Given angles:
- ∠A = 2x - 1
- ∠B = y + 5
- ∠C = 2y + 15
- ∠D = 4x - 7
Comparing the angles:
- To find the greatest angle, we need to compare the expressions for the angles given in terms of x and y.
- Given the expressions:
- ∠A = 2x - 1
- ∠B = y + 5
- ∠C = 2y + 15
- ∠D = 4x - 7
- To compare the angles, we need to find the values of x and y that would make the corresponding expressions largest.
- By comparing the expressions, we find that the largest expression is for ∠C = 2y + 15.
Therefore, the greatest angle of the quadrilateral is 2y + 15.
- We need to find the value of y that would make this expression largest.
- Since the value of y that makes the expression largest is the greatest angle of the quadrilateral, we need to solve for y.
- Comparing the expressions for ∠C = 2y + 15 with ∠B = y + 5:
- 2y + 15 > y + 5
- y > -10
- Therefore, the value of y that makes the expression 2y + 15 largest is y > -10.
- Substituting y = -10 into the expression 2y + 15:
- 2(-10) + 15 = -20 + 15 = -5
- Therefore, the greatest angle of the cyclic quadrilateral is 2y + 15 = 2(-5) + 15 = 10 + 15 = 25 degrees.
Hence, the greatest angle of the quadrilateral is 125 degrees (option C).
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Community Answer
In a cyclic quadrilateral ABCD, ∠A = 2x - 1, ∠B = y + 5, ∠...
In a cyclic quadrilateral,
∠A + ∠C = 180°, ∠B + ∠D = 180°
Here 2x - 1 + 2y + 15 = 180°
⇒ 2x + 2y = 166
x + y = 83 ...(1)
and 4x - 7 + y + 5 = 180°
⇒ 4x + y = 182 ...(2)
Solving eqns (1) and (2), we get x = 33, y = 50
∠A = 2x - 1 = 2 × 33 - 1= 65°
∠B = y + 5 = 50 + 5 = 55°
∠C = 2y + 15 = 2 × 50 + 15 = 115°
∠D = 4x - 7 = 4 × 33 - 7 = 125°
∠A + ∠C = 180°, ∠B + ∠D = 180°
Here 2x - 1 + 2y + 15 = 180°
⇒ 2x + 2y = 166
x + y = 83 ...(1)
and 4x - 7 + y + 5 = 180°
⇒ 4x + y = 182 ...(2)
Solving eqns (1) and (2), we get x = 33, y = 50
∠A = 2x - 1 = 2 × 33 - 1= 65°
∠B = y + 5 = 50 + 5 = 55°
∠C = 2y + 15 = 2 × 50 + 15 = 115°
∠D = 4x - 7 = 4 × 33 - 7 = 125°
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In a cyclic quadrilateral ABCD, ∠A = 2x - 1, ∠B = y + 5, ∠C = 2y + 15, ∠D = 4x - 7. Which is the greatest angle of quadrilateral.a)115°b)120°c)125°d)85°Correct answer is option 'C'. 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 In a cyclic quadrilateral ABCD, ∠A = 2x - 1, ∠B = y + 5, ∠C = 2y + 15, ∠D = 4x - 7. Which is the greatest angle of quadrilateral.a)115°b)120°c)125°d)85°Correct answer is option 'C'. 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 In a cyclic quadrilateral ABCD, ∠A = 2x - 1, ∠B = y + 5, ∠C = 2y + 15, ∠D = 4x - 7. Which is the greatest angle of quadrilateral.a)115°b)120°c)125°d)85°Correct answer is option 'C'. Can you explain this answer?.
In a cyclic quadrilateral ABCD, ∠A = 2x - 1, ∠B = y + 5, ∠C = 2y + 15, ∠D = 4x - 7. Which is the greatest angle of quadrilateral.a)115°b)120°c)125°d)85°Correct answer is option 'C'. 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 In a cyclic quadrilateral ABCD, ∠A = 2x - 1, ∠B = y + 5, ∠C = 2y + 15, ∠D = 4x - 7. Which is the greatest angle of quadrilateral.a)115°b)120°c)125°d)85°Correct answer is option 'C'. 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 In a cyclic quadrilateral ABCD, ∠A = 2x - 1, ∠B = y + 5, ∠C = 2y + 15, ∠D = 4x - 7. Which is the greatest angle of quadrilateral.a)115°b)120°c)125°d)85°Correct answer is option 'C'. Can you explain this answer?.
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