The bisector of the acute and right angles of a right-angled triangle intersect at an angle

The bisector of the acute and right angles of a right-angled triangle intersect at an angle of 130 °. Find the sharp corners of the triangle.

Since, by condition, AK is the bisector of the right angle, then the angle AOB = 90/2 = 45.

In the triangle AOB, we determine the value of the angle ABO. Angle ABO = (180 – AOB = AOB) = (180 – 45 – 130) = 15.

Since DВ is the bisector of the angle ABC, then the angle ABC = 2 * ABO = 2 * 15 = 30.

Then the angle ACB = (180 – BAC – ABC) = (180 – 90 – 30) = 60.

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