The diagonals of the rectangle intersect at an angle of 60 °. find the corners that form a diagonal with the sides of the rectangle.

Let’s say we have a rectangle ABСD, the intersection point is point O.
Consider a triangle AOB, in which the angle O is 60 degrees. If one angle in a triangle is 60 degrees. hence the other two angles are equal to 60 degrees. Ie angle BAO = ABO = 60 degrees.
Accordingly, we can consider the SOD triangle (everything is identical to the previous one)
Now consider the biofeedback triangle, the angle O in it is equal to 120 degrees. since the angles of ВOС and СOD are adjacent and together equal 180 degrees, and the angle of СOD is 60 degrees.
The angle BCO is 90-60 = 30 degrees, since the angle C in the rectangle is 90 degrees, and the angle is divided in half by the diagonal CA. which divides the angle into two angles: 0 and 30 degrees.
Conclusion: One angle between the diagonal and the side is 60, and the second 30