The bisector of a right angle of a right-angled triangle forms angles with the hypotenuse

The bisector of a right angle of a right-angled triangle forms angles with the hypotenuse, one of which is 70 °, find the angles of the angles of this triangle.

Since the segment CM is the bisector of the right angle, the angle AFM = BCM = 90/2 = 45.

Then in the AFM triangle the angle CAM = (180 – AFM – AMC) = (180 – 45 – 70) = 65.

The BMC angle is adjacent to the ABM angle, then BCM = (180 – 70) = 110.

In the BCM triangle, the CBM angle = (180 – 110 – 45) = 65.

Answer: The acute angles of the triangle are 25 and 65.