The middle line cuts off an isosceles right-angled triangle from this triangle. Find the corners of this triangle.

Let us prove that triangles ABC and CME are similar.

The angle B in triangles is common, the angle BAC is equal to the ВKM triangle as the corresponding angles at the intersection of parallel straight lines KM and AC secant AB. Then the ABC triangle is similar to the ВKM triangle in two angles.

Since the ВKM triangle is isosceles, the ВMC angle =ВKM.

For similar triangles, the corresponding angles of these triangles are equal.

Then the angle BAC = BCA = ВKM = ВMK.

Answer: The angles of the original triangle ABC are equal to the angles of the isosceles triangle ВKM.