To find the measure of angle \( m∠2 \), we can use the properties of angles formed by intersecting lines.
In the diagram described, angle 4 and angle 2 appear to be a pair of vertically opposite angles. Vertically opposite angles are equal, so:
\[ m∠2 = m∠4 \]
Given that \( m∠4 = 31° \), we can conclude that:
\[ m∠2 = 31° \]
Thus, the correct answer is \( 31° \).