For a line AB A. the forebearing of AB and back bearing of AB differ by 180° B. the forebearing of AB and back bearing of BA differ by 180° C. both (A) and (B) are correct D. none is correct

The correct answer is: A. the forebearing of AB and back bearing of AB differ by 180°.

The forebearing of a line is the angle between the north direction and the line, measured clockwise from north. The back bearing of a line is the angle between the south direction and the line, measured clockwise from south.

For a line AB, the forebearing of AB is the angle between the north direction and line AB, measured clockwise from north. The back bearing of AB is the angle between the south direction and line AB, measured clockwise from south.

Since the north direction is 0° and the south direction is 180°, the forebearing of AB and the back bearing of AB differ by 180°.

Option B is incorrect because the back bearing of BA is the angle between the south direction and line BA, measured clockwise from south. Since the south direction is 180° and the line BA is the same as the line AB, the back bearing of BA is 180°. The forebearing of AB is the angle between the north direction and line AB, measured clockwise from north. Since the north direction is 0° and the line AB is the same as the line BA, the forebearing of BA is 0°. Therefore, the forebearing of AB and the back bearing of BA do not differ by 180°.

Option C is incorrect because both (A) and (B) are not correct.

Option D is incorrect because the forebearing of AB and the back bearing of AB differ by 180°.