A man is facing west and turns anticlockwise by 90 degrees and moves 10 m straight, then he again turns 90 degrees anticlockwise. Which direction is the man facing now?

Introduction / Context:
This question concerns only the direction in which a man is facing after making two anticlockwise turns of 90 degrees each, starting from facing west. The distance he moves after the first turn does not change his orientation. Such problems assess understanding of rotational directions on the compass and do not require coordinate calculations.

Given Data / Assumptions:
- Initially the man is facing west. - He turns anticlockwise by 90 degrees and walks 10 m. - He then again turns 90 degrees anticlockwise. - All turns are right angle turns and there are no further movements after the second turn.

Concept / Approach:
Anticlockwise rotation on the compass moves from north to west, west to south, south to east and east to north. Starting from a given direction, each 90 degree anticlockwise turn simply shifts to the next direction in this sequence. The distance walked after the first turn does not change direction, so we only apply the rotations to deduce the final orientation. Counting these rotations carefully produces the correct answer quickly.

Step-by-Step Solution:
1. Initial direction: west. 2. First anticlockwise 90 degree turn from west moves him to face south. 3. He then walks 10 m while facing south, but his facing direction remains south. 4. Second anticlockwise 90 degree turn from south moves him to face east. 5. After this second turn, there is no additional movement mentioned, so his final facing direction is east.

Verification / Alternative check:
We can visualize this using a compass diagram: north at the top, east to the right, south at the bottom and west to the left. Place an arrow pointing left (west). Rotating it anticlockwise once points it downwards (south). Rotating it anticlockwise a second time points it to the right (east). This visual check immediately confirms the orientation without involving the 10 m movement at all.

Why Other Options Are Wrong:
- North would require three anticlockwise turns from west or equivalent rotation, which is not given. - West is the initial direction; two anticlockwise rotations cannot bring him back to west. - South is only the intermediate direction after the first turn, not the direction after the second turn. - North East is a diagonal direction that never appears in a sequence of right angle turns among cardinal directions.

Common Pitfalls:
Some learners confuse clockwise with anticlockwise rotation or mistakenly think in terms of their own left and right when observing from outside. It is important to fix the compass in mind and rotate consistently in the requested direction. Ignoring the unnecessary distance moved and focusing only on the sequence of turns helps avoid distraction and errors.

Final Answer:
After the two anticlockwise turns, the man is facing east.