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ABCD is a cyclic quadrilateral AB and DC are produced to meet at P. If ∠ADC = 70° and ∠DAB = 60°, then the ∠PBC + ∠PCB is (SSC CGL 2nd Sit. 2013)
- a)130°
- b)150°
- c)155°
- d)180°
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
ABCD is a cyclic quadrilateral AB and DC are produced to meet at P. If...
As ABCD is a cyclic quadrilateral.
In which
∠ADC = 70°
∠ABC = 180° – 70° = 110°
⇒ ∠PBC = 180° – 110° = 70°
And ∠DAB = 60°
∠BCD = 180° – 60° = 120°
⇒ ∠PCB = 180° – 120° = 60°
∴ ∠PBC + ∠PCB = 70° + 60° = 130°
Most Upvoted Answer
ABCD is a cyclic quadrilateral AB and DC are produced to meet at P. If...
As ABCD is a cyclic quadrilateral.
In which
∠ADC = 70°
∠ABC = 180° – 70° = 110°
⇒ ∠PBC = 180° – 110° = 70°
And ∠DAB = 60°
∠BCD = 180° – 60° = 120°
⇒ ∠PCB = 180° – 120° = 60°
∴ ∠PBC + ∠PCB = 70° + 60° = 130°
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ABCD is a cyclic quadrilateral AB and DC are produced to meet at P. If...
ABCD is a cyclic quadrilateral and AB and DC are produced to meet at P, then:
1) ∠ABP + ∠DCP = 180° (opposite angles in a cyclic quadrilateral)
2) ∠PAB + ∠PCD = 180° (opposite angles in a cyclic quadrilateral)
3) ∠ABP + ∠PAB = 180° (linear pair)
4) ∠DCP + ∠PCD = 180° (linear pair)
From equations 1) and 2), we can conclude that:
∠ABP + ∠DCP = ∠PAB + ∠PCD
From equations 3) and 4), we can conclude that:
∠ABP + ∠PAB = ∠DCP + ∠PCD
Combining the two equations, we get:
∠ABP + ∠DCP = ∠ABP + ∠PAB
Simplifying the equation, we get:
∠DCP = ∠PAB
Therefore, ∠DCP is equal to ∠PAB.
1) ∠ABP + ∠DCP = 180° (opposite angles in a cyclic quadrilateral)
2) ∠PAB + ∠PCD = 180° (opposite angles in a cyclic quadrilateral)
3) ∠ABP + ∠PAB = 180° (linear pair)
4) ∠DCP + ∠PCD = 180° (linear pair)
From equations 1) and 2), we can conclude that:
∠ABP + ∠DCP = ∠PAB + ∠PCD
From equations 3) and 4), we can conclude that:
∠ABP + ∠PAB = ∠DCP + ∠PCD
Combining the two equations, we get:
∠ABP + ∠DCP = ∠ABP + ∠PAB
Simplifying the equation, we get:
∠DCP = ∠PAB
Therefore, ∠DCP is equal to ∠PAB.
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ABCD is a cyclic quadrilateral AB and DC are produced to meet at P. If ∠ADC = 70° and ∠DAB = 60°, then the ∠PBC + ∠PCB is (SSC CGL 2nd Sit. 2013)a)130°b)150°c)155°d)180°Correct answer is option 'A'. Can you explain this answer?
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ABCD is a cyclic quadrilateral AB and DC are produced to meet at P. If ∠ADC = 70° and ∠DAB = 60°, then the ∠PBC + ∠PCB is (SSC CGL 2nd Sit. 2013)a)130°b)150°c)155°d)180°Correct answer is option 'A'. 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 ABCD is a cyclic quadrilateral AB and DC are produced to meet at P. If ∠ADC = 70° and ∠DAB = 60°, then the ∠PBC + ∠PCB is (SSC CGL 2nd Sit. 2013)a)130°b)150°c)155°d)180°Correct answer is option 'A'. 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 ABCD is a cyclic quadrilateral AB and DC are produced to meet at P. If ∠ADC = 70° and ∠DAB = 60°, then the ∠PBC + ∠PCB is (SSC CGL 2nd Sit. 2013)a)130°b)150°c)155°d)180°Correct answer is option 'A'. Can you explain this answer?.
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