Set the coordinates of point C as the origin coordinates, that is, (0,0), and then set up a space rectangular coordinate system with CA as the X axis and CB as the Y axis to get the coordinates of each point.
The cosine of the included angle between straight lines in different planes is the product of vectors divided by the product of the modules of two vectors.
The cosine of dihedral angle can be calculated by the included angle of normal vectors of two planes, which should be relatively easy.
This problem can be solved geometrically, but it may be more troublesome.
For example, in the first question, if the midpoint of AC is D, and the midpoint of A 1B is O, and DO is connected, there will be DOΣ CB 1, then the included angle between the straight lines BA 1 and CB1is equal to the angle DOB, so we only need to solve the triangle DOB, and we can get some information about the triangle DOB according to the known conditions.
The second problem is that if point C is perpendicular to A 1B and the vertical foot is E, if point C is perpendicular to AB 1B and point F intersects AB or BB 1, then the angle CEF is equal to the dihedral angle B-AB 1-C, and then it is indirectly calculated as.
That's the end of my answer, thank you.
I hope my answer is helpful to you.