You are facing East. You turn 45° in the clockwise direction and then 180° in…

The eight compass directions sit at fixed bearings measured clockwise from North — North = 0°, North-East = 45°, East = 90°, South-East = 135°, South = 180°, South-West = 225°, West = 270°, North-West = 315°. A clockwise turn increases the current bearing and an anti-clockwise turn decreases it, with the result taken modulo 360°.

1. Start facing East, so the starting bearing is 90°.

2. Turn 45° clockwise: 90° + 45° = 135°.

3. Turn 180° anti-clockwise: 135° − 180° = −45°, which is 315° after adding 360°.

4. Turn 270° clockwise: 315° + 270° = 585°, which is 225° after subtracting 360°.

5. A bearing of 225° is the South-West direction.

As a check, treat every clockwise turn as positive and every anti-clockwise turn as negative: the three turns combine to +45° − 180° + 270° = +135° net clockwise rotation from the starting East bearing. Adding this to 90° gives 90° + 135° = 225°, the same bearing obtained above.

Both methods place the final bearing at 225°, which is South-West.