Bearings: Convert a whole-circle bearing (W.C.B.) of 180° to the reduced (quadrantal) bearing format. State the correct reduced bearing for this exact due-south direction.

Introduction / Context:
Bearing systems in surveying are commonly expressed in two ways: whole-circle bearings (0° to 360° measured clockwise from true north) and reduced or quadrantal bearings (measured within 0° to 90° referenced to the nearest cardinal direction, N or S, and directed toward E or W). Converting between these is routine when reducing field notes or combining data from instruments and maps.

Given Data / Assumptions:

• Whole-circle bearing (W.C.B.) of the line is exactly 180°.
• Reduced (quadrantal) bearing is requested.
• Cardinal directions: N (0°/360°), E (90°), S (180°), W (270°).

Concept / Approach:

W.C.B. 180° points exactly to the south. In quadrantal form, directions exactly along a cardinal are written simply by the cardinal letter itself. Some texts also write S 0° E or S 0° W for the limiting case, both meaning the same due-south line. However, the most compact and standard reduced form for a pure cardinal line is just the cardinal letter, here S.

Step-by-Step Solution:

Verification / Alternative check:

Converting back: reduced S corresponds uniquely to W.C.B. 180°. This matches map and instrument conventions for cardinal bearings.

Why Other Options Are Wrong:

S 0° E and S 0° W are verbose forms sometimes seen but the canonical reduced form for a cardinal line is S. N is incorrect; “None” is unnecessary because S is valid.

Common Pitfalls:

Writing an arbitrary small angle with the cardinal when the value is exactly 180°; confusing W.C.B. with reduced bearing notation.

Final Answer:

S