In the ABCDA1B1C1D1 cube, define the angle between the crossing lines AC1 and A1B.

Line BA1 lies in the plane of the side face of the cube, but it also lies in the plane BA1D1C.
Plane BA1D1C is the plane in which the other diagonal of the cube lies – BD1.
Since the angle between the crossed lines does not depend on the choice of the point at which the lines intersect, we can choose any straight lines parallel to the crossed lines, the angle between which we need to find.
We know that the diagonals of any cube intersect at right angles, then the planes in which they lie also intersect at an angle of 90 °. This means that the angle between crossing lines BA1 and AC1 is also 90 °.
ANSWER: 90 °.