In a right-angled triangle ABC with a right angle C and an angle A = 22 degrees

In a right-angled triangle ABC with a right angle C and an angle A = 22 degrees, the bisector BB1 of the angle ABC is drawn. Find the angle of triangle ABB1 and triangle BB1C.

In triangle ABC, angle B = 90 ° – 22 ° = 68 °, bisector BB1 divides it into two equal angles:
angle B1BC = angle B1BA = 68 ° / 2 = 34 °.
Consider the triangle ABB1, in which two angles (A = 22 ° and B = 34 °) are known, and the angle B1 = 180 ° – (22 ° + 34 °) = 180 ° – 56 ° = 124 °.
Consider a triangle BB1C, in which two angles (C = 90 ° and B = 34 °) are known, and the angle B1 = 90 ° – 34 ° = 56 °.
Answer: angles of triangle ABB1: A = 22 °, B = 34 °, B1 = 124 °, angles of triangle BB1C C = 90 °, B = 34 °, B1 = 56 °