The bisectors of the acute angles of a right triangle meet at O, then the angle at O between the two bisectors is

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Solution

In right $Δ A B C, ∠ A = 90^{\circ}$

Bisectors of $∠ B$ and $∠ C$ meet at O, then

$∠ B O C = 90^{\circ} + \frac{1}{2} ∠ A$

= $90^{\circ} + \frac{1}{2} \times 90^{\circ} = 90^{\circ} + 45^{\circ} = 135^{\circ}$

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