Hello, daydreembelievr!
Suppose each edge is 6 inches long.
Find the measure of the angle formed by diagonal $\displaystyle GB$ and edge $\displaystyle GC$.
Triangle $\displaystyle BCG$ is a right triangle. Code:
* B
/|
/ |
/ | _
/ | 6√2
/ |
/ |
/ θ |
G *-------* C
6
$\displaystyle GC$ is an edge of the cube: .$\displaystyle GC \:=\:6$
$\displaystyle BC$ is the diagonal of a face: .$\displaystyle BC \:=\:6\sqrt{2}$
Then: .$\displaystyle \tan\theta\:=\:\frac{6\sqrt{2}}{6} \:=\:
\sqrt{2}\quad\Rightarrow\quad \theta \:\approx\:54.7^o$