The angles x deg a deg c deg and pi ndash b deg are indicated in the figure given below Wh...........

Quantitative Aptitude ( CCS) Geometry

The angles x°, a°, c° and (π – b)° are indicated in the figure given below. Which one of the following is correct?

x° = a° + c° – b°

x° = b° – a° – c°

x° = a° + b° + c°

x° = a° – b° + c°

∠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°.

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