Step 1: Understanding Back Bearing.
The back bearing is the opposite direction of the fore bearing. To calculate the back bearing, we add 180° to the fore bearing. If the result is greater than 360°, subtract 360°.
Step 2: Calculating the Back Bearing.
The fore bearing of line AB is 15°30'. The back bearing will be:
\[
\text{Back bearing} = 15°30' + 180° = 195°30'.
\]
Since the result is less than 360°, there is no need to subtract 360°.
Step 3: Conclusion.
Therefore, the back bearing of line AB is 195°30', making option (4) the correct answer.
Final Answer:
\[
\boxed{195°30'}
\]