Can the bisectors of two corners of a right triangle intersect at an angle of 40 degrees.

Consider a right-angled triangle ABC, and bisectors CН and BK, point O – the point of intersection of these bisectors, angles B and C at 45 degrees.
Find an acute angle O in the triangle НOB = KOС.
Consider triangles ABK and KOС.
Angle B in triangle ABK is 45/2 = 22.5 degrees.
Then the angle K = 180 – (90 + 22.5) = 67.5 degrees.
And then the angle K in the triangle KOC = 180 – 67.5 = 112.5 degrees.
The angle O in the triangle KOC = 180 – (112.5 + 22.5) = 45 degrees.
This means that the bisectors cannot intersect at an angle of 40 degrees.

Arguing similarly, we find that the bisectors do not intersect at an angle of 40 degrees if one of the bisectors goes out of the right angle. And the angle between the bisectors will be 180 – (180 – 90 – 22.5) = 67.5 degrees.