The man starts facing West.
Using a clockwise rotation system where angles are measured from North:
- North = 0°
- East = 90°
- South = 180°
- West = 270°
Starting position: West = 270°
First turn: 45° clockwise from West
270°+45°=315°
The man is now facing North-West.
Second turn: 180° clockwise from North-West
315°+180°=495°
495°−360°=135°
The man is now facing South-East.
Third turn: 270° anti-clockwise from South-East
Anti-clockwise rotation means subtracting the angle:
135°−270°=−135°
Converting to positive angle:
−135°+360°=225°
225° corresponds to South-West (halfway between South at 180° and West at 270°).
The man is now facing South-West.
Therefore, the answer is Option 2: South-West.