The diagonals of the rectangle intersect at an angle of 60 degrees. What are the angles of the diagonal of the rectangle with its sides?

For the solution, draw a rectangle, marking the vertices as MNHK.

The problem says that the diagonals of the rectangle MNHK intersect at an angle of 60 degrees at the point O.

Consider the MCO triangle, where the angle MOC = 60о, and the angles ОМК and ОКМ are equal, and these are the angles that the diagonal of the rectangle creates with its sides and they are equal to (180 – 60) / 2 = 60о.

Therefore, angles 60 ° and 90 – 60 = 30 ° create a diagonal of the rectangle with its sides.