Bearings — a line has reduced (quadrantal) bearing N 87° W. What is its whole circle bearing (WCB), measured clockwise from north (0°–360°)?

Introduction / Context:
Survey lines may be expressed either as reduced (quadrantal) bearings like N θ E/W or S θ E/W, or as whole circle bearings (WCB) measured 0°–360° clockwise from true or magnetic north. Converting correctly between these systems is essential for plotting, computations, and using different instruments consistently.

Given Data / Assumptions:

• Reduced bearing: N 87° W (i.e., 87° west of north).
• WCB is measured clockwise from north.
• Standard quadrant conventions apply.

Concept / Approach:
N 87° W lies in the northwest quadrant. From north (0°), rotating clockwise to the west side means passing through 360° back to just beyond it. The equivalent WCB is 360° − 87° = 273°. General rule: N θ W → WCB = 360° − θ; N θ E → θ; S θ E → 180° − θ; S θ W → 180° + θ.

Step-by-Step Solution:

Verification / Alternative check:
Sketch axes and mark 0° at north; move clockwise nearly to west (270°) and add 3° more: 273°, which matches the conversion.

Why Other Options Are Wrong:

• 87°: This would be N 87° E.
• 93°: Lies in NE quadrant; wrong side.
• 3°: Near north; not in NW quadrant.

Common Pitfalls:
Forgetting that N θ W and S θ E swap around 360° and 180° respectively; always visualize the quadrant.

Final Answer:
273°