In a ABC the sides AB and AC have been produced to D and E Bisectors of ang CBD and ang BCE meet at ...........

Quantitative Aptitude ( CCS) Geometry

In a ? ABC, the sides AB and AC have been produced to D and E. Bisectors of ∠ CBD and ∠ BCE meet at O. If ∠ A = 64°, then ∠ BOC is :

52°

58°

26°

112°

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Explanation:

∠CBD = ∠A + ∠C ,
∠BCE = ∠B + ∠A.
[? An exterior angle of a triangle is equal to the sum of the opposite interior angles.]
∴ ∠CBD + ∠BCE
= (∠A + ∠B + ∠C) + ∠A
= 180° + A
1/2 ∠CBD + 1/2 ∠BCE = 90° + A/2
But,
1/2 ∠CBD + 1/2 ∠BCE + ∠BOC
= 180°
∴ ∠BOC = 180° – (90° + A/2)
= (90° – A/2)
= (90° – 64/2)
= 58°