Question : In $△ A B C$ , the internal bisectors of $∠ B$ and $∠ C$ meet at point $O$ . If $∠ A = 80^{\circ}$ , then $∠ B O C$ is equal to:
Option 1: $100^{\circ}$
Option 2: $120^{\circ}$
Option 3: $130^{\circ}$
Option 4: $140^{\circ}$

Question

Question : In $△ A B C$ the internal bisectors of $∠ A B C$ and $∠ A C B$ meet at $X$ and $∠ B A C = 30^{\circ}$ . The measure of $∠ B X C$ is:
Option 1: $120^{\circ}$
Option 2: $115^{\circ}$
Option 3: $105^{\circ}$
Option 4: $150^{\circ}$

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Answer 1

Correct Answer: $130^{\circ}$

Solution :
Given: $∠ A = 80^{\circ}$
To find: $∠ B O C$
We know that,
Angle formed by internal bisectors of base angles = $90^{\circ} + \frac{1}{2} ∠ A$
⇒ $∠ B O C$ = $90^{\circ} + \frac{1}{2} ∠ A$
= $90^{\circ} + \frac{1}{2} \times 80^{\circ}$
= $90^{\circ} + 40^{\circ}$
= $130^{\circ}$
Hence, the correct answer is $130^{\circ}$ .

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Question : In △ABC, the internal bisectors of ∠B and ∠C meet at point O. If ∠A=80∘, then ∠BOC is equal to:Option 1: 100∘Option 2: 120∘Option 3: 130∘Option 4: 140∘

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Question : In $△ A B C$ , the internal bisectors of $∠ B$ and $∠ C$ meet at point $O$ . If $∠ A = 80^{\circ}$ , then $∠ B O C$ is equal to:
Option 1: $100^{\circ}$
Option 2: $120^{\circ}$
Option 3: $130^{\circ}$
Option 4: $140^{\circ}$