Find the angle between a diagonal of a cube and a diagonal of one of its faces.

35.26°

Step-by-step explanation:

If a cube has side length x

diagonal of the face = x*√2

The diagonal of the cube = x * √3

the angle between them is an acute angle in a right triangle,

opposite = x, adjacent = x*√2, hyp. = x*√3

sin (angle) = x / (x*√3)

angle = sin^ (-1) (1/√3) = 35.26