Given a cube ABCDA1B1C1D1 Find the angle between straight lines A1D and AB1.

The angle between the intersecting straight lines AB1 and A1D is equal to the angle between AB1 and the straight line that is parallel to the straight line A1D.

We draw a straight line B1C. Line B1C is obtained by parallel translation of line A1D by the length of the edge in the direction perpendicular to the plane of the side face AA1DD1, therefore it will be parallel to A1D. If you connect points A and C, then the straight lines AB1, B1C and AC form an equilateral triangle, as they are the diagonals of the sides of the cube. All the faces of the cube and all the diagonals of the faces are equal. In an equilateral triangle, all angles are 60 °, including the angle AB1C, which is equal to the angle between straight lines AB1 and A1D.

Correct answer: 60 °.




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