The sides BC, CA and AB of ΔABC are produced in order to form exterior angles �

Question

The sides BC, CA and AB of

Δ A B C

are produced in order to form exterior angles

∠ A C D

∠ B A F

and

∠ C B E

respectively, then

∠ B A F + ∠ A C D + ∠ C B E

Options:

A . 180∘

B . 270∘

C . 360∘

D . 540∘

Answer: Option C
:
C

By angle sum property,

x + y + z = 180^{\circ}

∠ B A F + ∠ A C D + ∠ C B E

= (180^{\circ} - x) + (180^{\circ} - y) + (180^{\circ} - z)

= 540^{\circ} - (x + y + z) = 540^{\circ} - 180^{\circ} = 360^{\circ}

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