BH is the height of an isosceles right triangle ABC drawn to the hypotenuse. Find the angles of triangle ABH.

Because the triangle is right-angled and isosceles, so the angle ABC = 90 °, and the angles BAC and BCA are equal to each other and equal to 45 ° because (180 ° -90 °) / 2 = 45 °
The BAH angle is equal to the BAC angle and is equal to 45 °. And also we have BH height, which means AC is perpendicular to BH, which means the angle BHA = 90 °.
Find the third angle: 180 ° -90 ° -45 ° = 45 °.
Answer: 45 ° 45 ° 90 °