Question

In a ΔABC, the internal bisectors of ∠B and ∠C meet at O. if ∠BAC = 72°, then the value of ∠BOC is:

• A. 110°
• B. 126°
• C. 136°
• D. 146°

Answer 1

Answer:

B. 126°

Solution:

Calculation : 

∠BAC = 72° 

By angle sum property 

⇒ ∠A + ∠B + ∠C = 180

 

⇒ ∠B + ∠C = 180 − 72 = 108

 

⇒ ∠OBC + ∠OCB = 54

 

The Angular bisectors Meet at O

 

So By Angle sum property ,

 

⇒ ∠OBC + ∠OCB + ∠BOC = 180

 

⇒ 54 + ∠BOC = 180

 

⇒ ∠BOC = 126

 

∴ The correct answer is 126°.