What direction are you facing at the moment, if you start by facing south-east and turn around $225^{\circ }$ anti-clockwise?

Let's track the angular rotation step by step:
1. Facing South-East initially.
2. Turning $135^{\circ }$ anti-clockwise brings you to face North.
3. You have $225^{\circ }-135^{\circ }=90^{\circ }$ left to turn anti-clockwise.
4. Turning $90^{\circ }$ anti-clockwise from North leaves you facing West.