In the rectangle, the middle perpendicular of the diagonal AC intersects the side BC at point K so that BK: KC

In the rectangle, the middle perpendicular of the diagonal AC intersects the side BC at point K so that BK: KC = 1: 2. What angles does the diagonal of a rectangle divide into its corner?

Consider an isosceles triangle AKC. AK \  KC, since AO \  OC (from the middle of point O, the perpendicular OK was restored). KС= AK = 2 (parts), BK = 1 (part). Consider a rectangle triangle ABK: AK = 2, and BK = 1. This can be the case if the leg ВK is opposite the angle <BAK = 30 degrees. <BKA = 90 – 30 = 60 (degrees). <AKC = 180 – <AKB = 180 – 60 = 120. So, between the AC diagonal and BC side <BCA = (180 – 120) / 2 = 30 (degrees)
So the AC diagonal divides the right angle into angles equal to 30 and 60 degrees.