In a right-angled triangle ABC (angle C is 90 degrees), the bisectors CD

In a right-angled triangle ABC (angle C is 90 degrees), the bisectors CD and A intersect at point O. Angle AOC is 105 degrees. Find the acute angles of triangle ABC

Since CD is the bisector of a right angle, the angle ACO = 90/2 = 45.

Consider the AOC triangle. The sum of the inner angles of the triangle is 180, then the angle OAC = (180 – AOC – ACO) = (180 – 105 – 45) = 30.

Since AM is the bisector of the angle BAC, then the angle BAC = 2 * OAC = 2 * 30 = 60.

The sum of the acute angles of a right-angled triangle is 90, then the angle ABC = (90 – BAC) = (90 – 60) = 30.

Answer: The acute angles of the triangle are 30 and 60.