Step 1: Back Bearing Explained.
The back bearing is the opposite direction of the fore bearing. Calculate it by adding 180° to the fore bearing. If the sum exceeds 360°, subtract 360°.
Step 2: Back Bearing Calculation.
Line AB has a fore bearing of 15°30'. The back bearing is:
\[
\text{Back bearing} = 15°30' + 180° = 195°30'.
\]
Since the result is below 360°, no subtraction is needed.
Step 3: Conclusion.
Thus, the back bearing of line AB is 195°30', making option (4) the correct answer.
Final Answer:
\[
\boxed{195°30'}
\]