Final answer:
Lines a, b, and c are parallel as they run along the x-axis. Lines that are mutually perpendicular imply that lines a and b, lines b and c, and lines c and d are perpendicular to each other. There's an inconsistency with the reference to a 270° angle, but lines c and d could be parallel if they are in phase.
Step-by-step explanation:
When evaluating whether lines are parallel or perpendicular, we must consider their directions relative to each other. Two lines are parallel if they run in the same direction, never intersecting, and they are perpendicular if they intersect to form a 90° angle.
Based on the given information:
- Lines a, b, and c being parallel to each other and all along the x-axis indicate that line a and line b (option a) are parallel, as well as line b and line c (option c) are parallel.
- Lines being mutually perpendicular means that line a and line b (option b), line b and line c (option d), and also line c and line d (option f) are perpendicular.
- The information from the reference about lines b and d being perpendicular and forming a 270° angle does not conform to the standard definition of perpendicular lines that should form a 90° angle. Therefore, it can be concluded that only line c and line d could possibly be parallel (option e), if they are in phase with each other.