In a right-angled triangle, the bisector of greatest angle intersects the hypotenuse at an angle of 80 degrees

In a right-angled triangle, the bisector of greatest angle intersects the hypotenuse at an angle of 80 degrees. find the sharp corners of the given triangle.

Let’s designate this right-angled triangle ABC, AB – hypotenuse. Obviously, in a right-angled triangle, the largest angle is a straight line, in our case the angle C. The bisector of angle C intersects the hypotenuse at point H. Consider the triangle ACН. In it, the following are known: the angle СНА = 80 ° (by condition), the angle АСН = 90 ° / 2 = 45 ° (СН is the bisector). Find the СAН angle:
∠ СAН = 180 ° – (80 ° + 45 °) = 55 °.
We find the angle B in the right-angled triangle ABC:
∠ B = 90 ° – ∠ A = 90 ° – 55 ° = 35 °.
Answer: Acute triangles have degrees 55 ° and 35 °.