A man starts walking towards the north. After walking 100 meters, he turns to…

In direction-sense questions, a turn changes the direction a person is facing, not their position on the map directly. On a standard compass arranged clockwise as North to East to South to West to North, a single right turn always rotates the facing direction by exactly 90 degrees clockwise -- this holds regardless of how far the person walks before or after the turn.

1. The man starts out facing north.

2. He walks 100 meters -- this changes only his position, not the direction he is facing.

3. He then turns to his right, i.e., 90 degrees clockwise from north.

4. Moving 90 degrees clockwise from north on the compass lands exactly on east.

This matches the clock analogy: if north corresponds to the 12 o'clock mark, a right turn moves the facing hand to the 3 o'clock mark, which is east -- confirming the direction found above. Walking a further 50 meters after the turn only changes his position again, not the direction he faces.

So, the man is now facing east.