Bearings — if a line has whole circle bearing (WCB) 120°, what is its reduced (quadrantal) bearing?

Introduction / Context:Reduced bearings express directions within one of four quadrants relative to north or south. Converting accurately from whole circle bearings (0°–360° clockwise from north) to reduced bearings is a routine but crucial task in plotting and computations.

Given Data / Assumptions:

• WCB = 120°.
• WCB is measured from north, clockwise.
• Reduced bearing should be stated as N/S θ E/W.

Concept / Approach:Angles 90°–180° lie in the southeast (SE) quadrant. The reduced bearing equals S (180° − WCB) E. Here, 180° − 120° = 60°, so the reduced bearing is S 60° E.

Step-by-Step Solution:

Verification / Alternative check:Sketching the axes confirms the direction: 30° beyond east towards south does not fit; it is indeed 60° east of south.

Why Other Options Are Wrong:

• S 20° E: Wrong magnitude.
• N 120° E / N 60° E: These lie in NE quadrant, not SE.

Common Pitfalls:Confusing which reference (north or south) to use per quadrant; 90°–180° always references south.

Final Answer:S 60° E