Given that,

Arc AXB = Arc BYC (i)

Since,

Arc AXBYC is the arc equal to half circumference

And,

Angle subtended by half circumference at centre is 180°

Arc AXBYC = Arc AXB + Arc BYC

Arc AXBYC = Arc BYC + Arc BYC

Arc AXBYC = Arc AXBYC

Now,

∠BOC = ∠AOC

∠BOC = * 180°

∠BOC = 120°