In a right-angled triangle ABC with right angle C, the outside angle at apex A is 125 °. Find the angle ABC.

First way.

The external angle of a triangle is equal to the sum of the two internal angles of the triangle that are not adjacent to it.

Angle ВAD = (ACB + ABC).

Angle ABC = ВAD – AСB = 125 – 90 = 35.

Second way.

The angle BAC is adjacent to the angle ВAD, the sum of which is 1800, then the angle BAC = (180 – ВAD) = (180 – 125) = 55.

The sum of the acute angles of a right-angled triangle is 900, then the angle ABC = (90 – BAC) = (90 – 55) = 35.

Answer: The angle ABC is 350