Question

Find, to the nearest tenth of a degree, the
angle formed by the two main diagonals of a
cube that connect consecutive vertices of the
lower base to the opposite consecutive
vertices of the upper base, as illustrated at
right.

Answer 1

can't see your diagram, but consider the vectors representing the diagonals. If it's a unit cube, they might be joining
(0,0,0) and (1,1,1) = <1,1,1>
(1,1,0) and (0,0,1) = <-1,-1,1>
(1,0,0) and (0,1,1) = <-1,1,1>
...
Now just take the dot product of the two diagonals you are interested in and

u•v = 3cosθ