Question : In a $\triangle ABC$, the bisectors of $\angle$ABC and $\angle$ACB intersect each other at point O. If the $\angle$BOC is 125°, then the $\angle$BAC is equal to:
Option 1: 75°
Option 2: 78°
Option 3: 70°
Option 4: 82°
Correct Answer: 70°
Solution :
Given:
$\angle$BOC $=\ 125^\circ$
BO and OC is angle bisector.
Now,
By angle bisector theorem
$\Rightarrow \angle BOC\ =\ 90^\circ\ +\ \frac{1}{2}\angle BAC$
$\Rightarrow 125^\circ\ =\ 90^\circ\ +\ \frac{1}{2}\angle BAC$
$\Rightarrow \angle BAC\ =\ 70^\circ$
Hence, the correct answer is 70°
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