Direction Sense — Starting facing East, turn 100° clockwise and then 145° anti-clockwise. After these two turns, which compass direction will you finally face?

Introduction / Context:
Direction-sense problems ask you to track orientation after a sequence of turns. We will convert each turn into an angle relative to the starting facing (East) and simplify carefully, keeping clockwise and anti-clockwise signs consistent.

Given Data / Assumptions:

• Initial facing: East.
• First turn: 100° clockwise.
• Second turn: 145° anti-clockwise (i.e., opposite direction to clockwise).
• We treat clockwise as + and anti-clockwise as − relative to the current facing (or use a consistent angular system and subtract/ add appropriately).

Concept / Approach:
Normalize angles to one full circle. A helpful scheme is: East = 0°, South = 90°, West = 180°, North = 270° (or −90°). Clockwise moves increase the angle; anti-clockwise moves decrease it. Reduce the final angle modulo 360° and map back to a compass direction.

Step-by-Step Solution:
Start at East = 0°.Clockwise 100° → 0° + 100° = 100°. (Between South (90°) and West (180°) — i.e., South-West quadrant.)Anti-clockwise 145° → 100° − 145° = −45°.Normalize: −45° = 360° − 45° = 315°.315° lies between North (270°) and East (360°), i.e., North-East.

Verification / Alternative check:
Think in net rotation: +100° − 145° = −45°, which is a 45° turn anti-clockwise from East, landing in the North-East quadrant. Both methods agree.

Why Other Options Are Wrong:

• East: would require net 0°.
• North: would require net 270° or −90°.
• South-West: corresponds to around 225°; that was only after the first turn, not the final state.
• None of these: unnecessary because a listed option matches.

Common Pitfalls:
Mixing sign conventions or forgetting to normalize negative angles. Always compute net rotation and then map to a compass point.

Final Answer:
North-East