As shown in the figure △ABC, the bisector of ∠ABC and ∠ACB intersects at point O, if ∠ BOC = 120, ∠ A = 60.

Proof: as shown in the figure.

Because BOC = 120.

So ∠ OBC+∠ OCB =180-120 = 60.

And because the bisector of ∠ABC and ∠ACB intersects at point O.

So ∠ABC+∠ACB=60*2= 120.

So ∠ A = 180- 120 = 60.