In an isosceles right-angled triangle ABC, point O is a point. intersection of bisectors of right and acute angles

In an isosceles right-angled triangle ABC, point O is a point. intersection of bisectors of right and acute angles. define a smaller angle between these bisectors.

Since the triangle ABC is rectangular and isosceles, the angle ABC = 900, the angle BAC = BCA = (180 – 90) / 2 = 45.

The bisector of the angle of the BCA divides it in half, then the angle ACK = BCA / 2 = 45/2 = 22.5.

The bisector ВН is also the height of the triangle, then the AtoN triangle is rectangular.

In the right-angled triangle СНО, the angle СН = (180 – СНО – НСО) = 180 – 90 – 22.5 = 67.5.

Answer: The smaller angle between the bisectors is 67.5.