Final answer:
If ∠2 corresponds to ∠5 in quadrilateral ABCD with parallel lines AB and CD, then the measure of ∠5 is also 31°.
Step-by-step explanation:
To find the measure of m∠5 in quadrilateral ABCD, where AB parallel to CD and the measure of m∠2 is 31°, there are a few principles to consider. Because AB is parallel to CD, then corresponding angles are equal. Therefore, if ∠2 corresponds to ∠5, then m∠5 is also 31°. Without additional context or a diagram, we can not define the relationship between ∠2 and ∠5 precisely. However, the principle of corresponding angles in parallel lines implies that if ∠2 and ∠5 are in the corresponding position, then ∠5 will be equal to the measure of ∠2, which is 31°.