I am facing East. I turn 100° in the clockwise direction and then 145° in the…

Concept

Compass bearings are measured clockwise from North (North = 0°, East = 90°, South = 180°, West = 270°). Turning clockwise increases the bearing and turning anticlockwise decreases it; several turns combine into one net turn by adding clockwise amounts and subtracting anticlockwise amounts, keeping a consistent sign.

Application

1. Facing East corresponds to a bearing of 90°.

2. Turning 100° clockwise increases the bearing: 90° + 100° = 190°.

3. Turning 145° anticlockwise decreases the bearing: 190° − 145° = 45°.

4. A bearing of 45° lies exactly midway between North (0°) and East (90°), which is the compass direction North-East.

Cross-check

Equivalently, the two turns combine into a single net turn of 145° − 100° = 45° anticlockwise (since the anticlockwise turn is the larger of the two). Rotating the starting direction, East, by 45° anticlockwise gives the same result: North-East.

The final facing direction is North-East.