Question : In $\triangle ABC$, the internal bisectors of $\angle B$ and $\angle C$ meet at point $O$. If $\angle A = 80^\circ$, then $\angle BOC$ is equal to:
Option 1: $100^\circ$
Option 2: $120^\circ$
Option 3: $130^\circ$
Option 4: $140^\circ$
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Correct Answer: $130^\circ$
Solution :
Given: $\angle A = 80^\circ$
To find: $\angle BOC$
We know that,
Angle formed by internal bisectors of base angles = $90^\circ+\frac{1}{2}\angle A$
⇒ $\angle BOC$ = $90^\circ+\frac{1}{2}\angle A$
= $90^\circ+\frac{1}{2}×80^\circ$
= $90^\circ+40^\circ$
= $130^\circ$
Hence, the correct answer is $130^\circ$.
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