Answer
$54^{\circ}$
Work Step by Step
Let $d$ be the diagonal of the cube.
$d= (1,1,1)-(0,0,0)=(1,1,1)$
Let $a$ be the adjacent edge of the cube.
Then: $a=(0,0,1)$
The angle between two vectors can be calculated as:
$\cos \theta =\dfrac{m \cdot n}{||m||||n||}$
Now, $d \cdot a =(1,1,1) \cdot (0,0,1)=1$
and $||d||||a||=\sqrt{3}(1)=\sqrt3$
Thus, $\cos \theta =\dfrac{1}{\sqrt 3}$
or, $\theta =\cos^{-1}(\dfrac{1}{\sqrt 3})=54^{\circ} $
