A man facing South-East makes three turns of $90^{\circ }$ in the anticlockwise direction and then two $45^{\circ }$ turns in the clockwise direction. In which direction is his right hand now with respect to him?

Step-by-step angle evaluation:
1. Initial heading $=$ South-East.
2. Anticlockwise movement $=3\times 90^{\circ }=270^{\circ }$ anticlockwise.
3. Clockwise movement $=2\times 45^{\circ }=90^{\circ }$ clockwise.
4. Net effective movement $=270^{\circ }\text{ (anticlockwise)}-90^{\circ }\text{ (clockwise)}=180^{\circ }\text{ anticlockwise}$.

A rotation of $180^{\circ }$ completely reverses the direction, meaning the man is now facing North-West.
The right hand points $90^{\circ }$ clockwise relative to the facing direction. Rotating $90^{\circ }$ clockwise from North-West points directly to the North-East direction.