If you are facing towards the North and you turn 270 degrees anti-clockwise,…

When you rotate anti-clockwise from any cardinal direction, you move through the compass cycle North to West to South to East to North, one quarter-turn (90 degrees) at a time. A 270-degree anti-clockwise turn is therefore three of these quarter-turns in that cycle (270 / 90 = 3).

1. Starting direction: North.

2. First 90-degree anti-clockwise turn (total 90 degrees): facing West.

3. Second 90-degree anti-clockwise turn (total 180 degrees): facing South.

4. Third 90-degree anti-clockwise turn (total 270 degrees): facing East.

As an independent check, turning 270 degrees anti-clockwise is the same as turning 360 - 270 = 90 degrees clockwise from the same starting direction. A single 90-degree clockwise turn from North leads to East, which confirms the result.

So, starting from North and turning 270 degrees anti-clockwise, you end up facing East.