In the fig given, ∠A = 74° , ∠ ABC = 64° . If BO and CO are the bisectors of ∠ ABC and ∠ ACB. Then find ∠OCB and ∠BOC.

Given: ∠A = 74° , ∠ ABC = 64°

To find: ∠OBC and ∠BOC.

Explanation:

In Δ ABC,

By angle sum property:

∠A + ∠ ABC + ∠ ACB = 180°

⇒ 74° + 64°+ ∠ ACB = 180°

⇒ 138° + ∠ ACB = 180°

⇒ ∠ ACB = 42°

As ∠OBC = 1/2 ∠ ABC

So,

⇒∠OBC = 1/2 (64°)

= 32°

Similarly,

∠OCB = 1/2 ∠ ACB

⇒∠OCB = 21°

In ΔOBC,

By angle sum property:

∠OBC + ∠BOC + ∠ OCB = 180°

⇒ ∠OBC + ∠BOC + ∠ OCB = 180°

⇒32° + ∠BOC + 21° = 180°

⇒ 53° + ∠BOC = 180°

⇒ ∠BOC = 127°

Hence values of ∠OBC and ∠BOC are 21° and 127°.