Question : In $\triangle$ABC, $\angle$A = 66°. AB and AC are produced at points D and E, respectively. If the bisectors of $\angle$CBD and $\angle$BCE meet at the point O, then $\angle$BOC is equal to:
Option 1: $66^{\circ}$
Option 2: $93^{\circ}$
Option 3: $57^{\circ}$
Option 4: $114^{\circ}$
Correct Answer: $57^{\circ}$
Solution :
According to the question,
⇒ Exterior angle bisector = 90° – $\frac{1}{2}$ × opposite vertex angle
Now,
⇒ $\angle$BOC = 90° – $\frac{\angle A}{2}$ = 90° – $\frac{66°}{2}$ = 90° – 33° = 57°
Hence, the correct answer is 57°.
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