Rani faces towards the north. She turns 45 degrees in the clockwise direction…

Concept: When you turn through an angle, your facing shifts by that angle in the direction of the turn (clockwise increases the compass bearing, anti-clockwise decreases it). A special case: a 180-degree turn, whether clockwise or anti-clockwise, always lands you facing the exact opposite direction, because both routes reach the same final bearing.

Application:

1. Rani starts facing North (bearing 0 degrees).

2. She turns 45 degrees clockwise: 0 + 45 = 45 degrees, which is North-East.

3. She then turns 180 degrees anti-clockwise from North-East: 45 - 180 = -135, which is the same bearing as 225 degrees, i.e. South-West.

Cross-check: A 180-degree turn always results in the exact opposite direction, regardless of whether it is made clockwise or anti-clockwise. The opposite of North-East is South-West, which matches the step-by-step result above.

So Rani ends up facing South-West.