Let's interpret the given angle positions. Let the transversal intersect line $l$ at point $A$ and line $m$ at point $B$. Angle $3x$ is exterior above line $l$. Let's assume it's the top-left exterior angle. Angle $x$ is interior below line $l$. For a valid solution, we assume it's the bottom-right interior angle at line $l$. The interior angle adjacent to the exterior angle $3x$ (top-left) is $180^{\circ} - 3x$. This is the top-left interior angle. Since lines $l$ and $m$ are parallel, the alternate interior angles are equal. The top-left interior angle and the bottom-right interior angle are alternate interior angles. Therefore, $180^{\circ} - 3x = x$. $180^{\circ} = 4x$ $x = \frac{180^{\circ}}{4}$ $x = 45^{\circ}$. Now, angle $w$ is interior below line $m$. Let's assume it's the bottom-right interior angle at line $m$. Since $l || m$, the corresponding angles are equal. The bottom-right interior angle at line $l$ is $x$, and the bottom-right interior angle at line $m$ is $w$. Therefore, $w = x$. Substituting the value of $x$, we get $w = 45^{\circ}$.