Final answer:
If a line intersects two lines l and m, each at a 42° angle, then the lines l and m are parallel since alternate interior angles are equal when lines are A) parallel.
Step-by-step explanation:
When a line intersects two lines l and m, forming a 42° angle with each line, the possible relationships between lines l and m can be determined through the concept of alternate interior angles. If the two angles of 42° each are on opposite sides of the intersecting line, and are inside the space between lines l and m, and lines l and m are not perpendicular to the intersecting line, then lines l and m must be parallel. This is because alternate interior angles are equal in measure when the lines are parallel. There is no way for the two lines to be perpendicular in this case since perpendicular lines with a transversal would form a 90° angle, not a 42° angle. Therefore, the correct answer is A) Parallel.