Facing West, you turn 45° clockwise, then 180° clockwise again, and finally 270° anti-clockwise. After all these turns, what direction are you facing?

Introduction / Context:This item checks cumulative turn tracking. You must add clockwise rotations and subtract anti-clockwise rotations, then map the resulting angle to a compass direction.

Given Data / Assumptions:

• Initial facing: West.
• Turns: +45° clockwise, +180° clockwise, −270° anti-clockwise.
• Compass mapping (one convenient scheme): East = 0°, South = 90°, West = 180°, North = 270°.

Concept / Approach:Convert the initial facing to an angle, accumulate signed turns, reduce modulo 360°, and interpret the quadrant.

Step-by-Step Solution:West corresponds to 180°.After +45°: 180° + 45° = 225°.After +180°: 225° + 180° = 405° → 405° − 360° = 45°.After −270°: 45° − 270° = −225° → add 360° → 135°.135° lies between South (90°) and West (180°): that is South-West.

Verification / Alternative check:Combine the turns first: total rotation = +45° + 180° − 270° = −45°. From West (180°), −45° gives 135°, i.e., South-West. Same result.

Why Other Options Are Wrong:

• South: 90° exact; we have 135°.
• West: 180° exact; not our final bearing.
• North-West: 315° or around that quadrant; not matching 135°.
• None of these: incorrect since South-West fits.

Common Pitfalls:Forgetting to wrap angles within 0°–360° or mixing the sign of anti-clockwise rotation.

Final Answer:south-west