The diagonals of the rectangle CDEF intersect at point O. Find the angle between the diagonals if the CDO angle is 40 degrees.

In a rectangle, the diagonals, by their intersection, form two pairs of isosceles triangles. Consider one of the isosceles triangles, the CDO triangle, in which we know the angle at the base by condition.
Angle CDO = angle DCO = 40 ° (angles at the base of an isosceles triangle).
Let’s find the angle DOC, which is one of the angles between the diagonals:
DOC angle = 180 ° – (40 ° + 40 °) = 180 ° – 80 ° = 100 °.
The adjacent angle DOE = 180 ° – 100 ° = 80 °.
Answer: The diagonals intersect at angles of 100 ° and 80 °.