The man starts facing south. He then turns 135° in the anticlockwise direction. This means he is turning towards the east by 135° from his current direction. After this, he turns 180° in the clockwise direction. This means he is turning back in the opposite direction by 180° from his current direction.
To determine the final direction the man is facing, we need to find the net angle of rotation. The anticlockwise direction is positive (+) and the clockwise direction is negative (-).
From the starting point, the man turned 135° in the anticlockwise direction (+135°) and then turned 180° in the clockwise direction (-180°).
Therefore, the net angle of rotation is 135° + (-180°) = -45°.
To find the final direction, we need to imagine the directions in a compass. Starting from south, if we rotate 45° in the clockwise direction, we reach the south-west direction.
Hence, the man is facing south-west after his turns.
Therefore, the correct answer is option 4 - South-west.