(4) Given that line $l$ forms a $45^{\circ}$ angle with plane $\alpha$, and line $m \subset \alpha$, if the projection of line $l$ on $\alpha$ also forms a $45^{\circ}$ angle with line $m$, then the angle formed by line $l$ and $m$ is $\qquad$
(4) $60^{\circ}$ Hint: Draw $A O \perp \alpha$ at $O, A \in l$, connect $O B$, then $\angle A B O=45^{\circ}$

In $\alpha$, draw $B C$ making a $45^{\circ}$ angle with $O B$, then $B C / / m$, draw $O C \perp B C$ at $C$, connect $A C$, then $A C \perp B C$.

Let $O A=O B=1$, then $A B=\sqrt{2}, O C=$ $C B=\frac{\sqrt{2}}{2}$, so
$$
\cos \angle A B C=\frac{C B}{A B}=\frac{\frac{\sqrt{2}}{2}}{\sqrt{2}}=\frac{1}{2},
$$

thus $\angle A B C=60^{\circ}$.