5. Find the angle between the diagonal of a cube and the edge it meets at a vertex.

Answer 1

make a sketch
so you have a right-angled triangle
where the base of the triangle is the diagonal of the base of the cube
and the height of the triangle is the height of the cube
let the height of the cube be 1 unit
then the diagonal of the base is √2
let the angle be x
tanx = 1/√2
x = appr 35.26°

Here is another way using vectors:
https://www.youtube.com/watch?v=gUOBMUvtvfQ

Answer 2

if you mean the main diagonal of the cube, then google can provide you with several discussions.