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The angles x°, a°, c° and (π – b)° are indicated in the figure given below. Which one of the following is correct?
  • a)
    x° = a° + c° – b°
  • b)
    x° = b° – a° – c°
  • c)
    x° = a° + b° + c°
  • d)
    x° = a° – b° + c°
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The angles x°, a°, c° and (π– b)° are indicat...
∠PCT + ∠PCB = π
(Linear pair)
∠PCB = π – (π – b°) = b° ..... (i)

In ΔBPC,
∠PCB + ∠BPC + ∠PBC = π
∠PBC = π – ∠PCB – ∠BPC  =  π – b° – a° ..... (ii)
∵ ∠ABE + ∠EBC = π
(∵ ∠PBC = ∠EBC)      (linear pair)
∠ABE = π – ∠PBC = π – (π – b° – a°)  =  a° + b° ...(iii)
Now, in ΔABE
Sum of two interior angles = Exterior angle
∠EAB + ∠ABE = ∠BES ⇒ c° + b° + a° = x°
∴   x° = a° + b° + c°.
Hence, option C is correct.
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Most Upvoted Answer
The angles x°, a°, c° and (π– b)° are indicat...
∠PCT + ∠PCB = π
(Linear pair)
∠PCB = π – (π – b°) = b° ..... (i)

In ΔBPC,
∠PCB + ∠BPC + ∠PBC = π
∠PBC = π – ∠PCB – ∠BPC  =  π – b° – a° ..... (ii)
∵ ∠ABE + ∠EBC = π
(∵ ∠PBC = ∠EBC)      (linear pair)
∠ABE = π – ∠PBC = π – (π – b° – a°)  =  a° + b° ...(iii)
Now, in ΔABE
Sum of two interior angles = Exterior angle
∠EAB + ∠ABE = ∠BES ⇒ c° + b° + a° = x°
∴   x° = a° + b° + c°.
Hence, option C is correct.
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