In a right-angled triangle ABC with a right angle C and angle A = 18 degrees, the bisector BB1 of angle ABC

In a right-angled triangle ABC with a right angle C and angle A = 18 degrees, the bisector BB1 of angle ABC is drawn. find the angles of triangle ABB1 and triangle BB1C.

The sum of the acute angles of a right-angled triangle is 90, then the angle ABC = (90 – BAC) = (90 – 18) = 72.

BB1 is the bisector of the angle ABC, then the angle ABB1 = CBB1 = ABC / 2 = 72/2 = 36.

Angle AB1B = (180 – ABB1 – BAC) = 180 – 36 – 18 = 126.

Angle BB1C = (90 – BCB1) = (90 – 36) = 54.

Answer: The angles of triangle ABB1 are 18, 36, 128, the angles of triangle BB1C are 36, 54, 90.