Final answer:
The answer is b) East. A man initially facing North turns 135 degrees anticlockwise to face Southeast, then 180 degrees clockwise to face Northwest.
Step-by-step explanation:
The question involves determining the final direction a man is facing after two rotational movements. Originally, he is facing North. After turning 135 degrees in the anticlockwise direction, he will be facing Southeast. This is because a 90 degrees anticlockwise turn would have him facing East, and an additional 45 degrees anticlockwise takes him to Southeast. He then turns 180 degrees clockwise, which is equivalent to making a half-circle turn from his current direction. Therefore, from Southeast, a 180 degrees clockwise rotation would have him facing in the Northwest direction.
To determine the direction the man is facing, we need to calculate the net angular displacement after the two turns. The first turn is 135 degrees anticlockwise, which means the man is now facing West. The second turn is 180 degrees clockwise, which is equivalent to turning halfway around in the opposite direction. So, after the second turn, the man is facing the opposite direction of West, which is East.