Question: Given $l \parallel m \parallel n$, find the value of $x$. $x^\circ$ $137^\circ$ Three parallel lines labeled $l$, $m$, and $n$ run from lower left to upper right; a diagonal transversal slopes from upper left to lower right across all three lines. The $x^\circ$ angle is at the upper intersection on the left side of the transversal above line $l$ (top-left). The $137^\circ$ angle is at the middle intersection above line $m$ and to the right of the transversal (center).

1. **State the problem:** We have three parallel lines $l \parallel m \parallel n$ cut by a transversal. We are given an angle of $137^\circ$ at the middle intersection (above line $m$ and right of the transversal) and need to find the angle $x^\circ$ at the top intersection (above line $l$ and left of the transversal). 2. **Recall the properties of parallel lines and transversals:** - Corresponding angles are equal. - Alternate interior angles are equal. - Consecutive interior angles are supplementary (sum to $180^\circ$). 3. **Identify the relationship between the given $137^\circ$ angle and the angle adjacent to it:** Since the $137^\circ$ angle is above line $m$ and to the right of the transversal, the angle adjacent to it on the left side of the transversal at the same intersection is its supplementary angle: $$ 180^\circ - 137^\circ = 43^\circ $$ 4. **Use corresponding angles:** The $43^\circ$ angle on the left side of the transversal above line $m$ corresponds to the angle $x^\circ$ on the left side of the transversal above line $l$ because $l \parallel m$ and the transversal crosses them. Therefore, $$ x = 43^\circ $$ 5. **Final answer:** $$ x = 43^\circ $$