A man is facing west. He turns 45 degrees in the clockwise direction, then…

Concept: The eight standard compass directions sit 45° apart in a fixed clockwise cycle: North, North-East, East, South-East, South, South-West, West, North-West, and back to North. Turning “clockwise” by some angle moves forward through this cycle by that many 45° steps; turning “anticlockwise” moves backward through the same cycle by that many steps.

Step-by-step: Track each turn in order, starting from West.

1. Start facing West.

2. Turn 45° clockwise: one step forward from West in the cycle gives North-West.

3. Turn a further 180° clockwise: that is four more steps forward (180÷45 = 4) from North-West — North-West → North → North-East → East → South-East. So the heading is now South-East.

4. Turn 270° anticlockwise: that is six steps backward (270÷45 = 6) from South-East — South-East → East → North-East → North → North-West → West → South-West. So the final heading is South-West.

Cross-check: Taking clockwise turns as positive, the net rotation is +45° + 180° − 270° = −45°, i.e. a net 45° anticlockwise turn from the start. Moving one step backward from West in the cycle also gives South-West, confirming the step-by-step result.

Result: The man is now facing South-West.