The two horizontal lines are parallel. Find the value of m. The angle 111 degrees and the angle 3m are alternate exterior angles.

Step 1: Identify the relationship between the given angles.
The two horizontal lines are parallel, as indicated by the arrows. The diagonal line is a transversal.
The angle $111^\circ$ is an exterior angle located above the top parallel line and to the right of the transversal.
The angle $3m$ is also an exterior angle located below the bottom parallel line and to the left of the transversal.
These two angles are alternate exterior angles.

Step 2: Apply the property of alternate exterior angles.
When two parallel lines are intersected by a transversal, alternate exterior angles are equal.
Therefore, we can set the two angles equal to each other:

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