Longitude difference between two places: identify the correct rule(s) for computing the difference in longitudes depending on hemispheres.

Introduction / Context:
Accurate computation of longitude differences is fundamental in navigation, astronomy, and geodetic computations. Depending on whether locations lie in the same or opposite hemispheres (east or west), the arithmetic changes to obtain the smallest longitudinal separation.

Given Data / Assumptions:

• Longitudes measured east or west from Greenwich (0° to 180°E/W).
• Interest is in the minimal angular separation along parallels.
• All values expressed in degrees for simplicity.

Concept / Approach:
When both places are in the same hemisphere (both E or both W), the absolute difference gives the longitude separation. When they are in opposite hemispheres, the separation is the sum of magnitudes. If the computed separation exceeds 180°, its supplement to 360° represents the shorter path across the globe.

Step-by-Step Solution:
Case 1: Same hemisphere → Δλ = |λ1 − λ2|.Case 2: Opposite hemispheres → Δλ = |λ1| + |λ2|.Case 3: If Δλ > 180° → Use 360° − Δλ for the smaller arc.

Verification / Alternative check:
Test with examples (e.g., 170°E and 170°W): naive sum is 340°, but true smallest separation is 360° − 340° = 20°.

Why Other Options Are Wrong:
Each individual rule is correct, so “All the above” is the most complete choice.

Common Pitfalls:
Forgetting to reduce to the smaller arc; mixing E/W signs; not converting minutes/seconds consistently.

Final Answer:
All the above