Let ABC is an acute angled triangle.

∠B = 90^o

We know that,

∠A + ∠B + ∠C = 180^o

∠A + 90^o + ∠C = 180^o

∠A + ∠C = 90^o (i)

In

∠AOC + ∠ACD + ∠CAD = 180^o

∠AOC + ∠C + ∠A = 180^o

∠AOC + (∠A + ∠C) = 180^o

∠AOC + * 90^o = 180^o [From (i)]

∠AOC + 45^o = 180^o

∠AOC = 180^o – 45^o

= 135^o

Thus, the angle at O between two bisectors is equal to 135^o.