The question asks to identify the correct relationship between Whole Circle Bearing (WCB) and Quadrantal Bearing (QB) for specific quadrants.

Understanding Bearing Systems

Whole Circle Bearing (WCB): Measured clockwise from the North direction, ranging from 0° to 360°.

Quadrantal Bearing (QB): Measured from the North or South meridian towards East or West, always an acute angle (0° to 90°), denoted with quadrant (e.g., N 30° E, S 45° W).

Analyzing Quadrant Relationships

Let's determine the formula for the South-West (S-W) quadrant (WCB between 180° and 270°):

• In the S-W quadrant, WCB is measured clockwise from North, past East (90°) and South (180°).
• QB for S-W is measured from the South meridian towards the West.
• The angle measured from South towards West is the difference between the WCB and the South meridian (180°).
• Therefore, the value of QB is $WCB - 180°$. The notation is S $(WCB - 180°)$ W.

This matches statement 1: For the quadrant S-W, QB = WCB -180°.

Evaluating Other Options

• Option 2 (S-W, WCB = 180° – QB): This is incorrect. Rearranging the correct formula (QB = WCB - 180°), we get WCB = QB + 180°.
• Option 3 (N-W, WCB = 180° - QB): This is incorrect. For the N-W quadrant (WCB 270° to 360°), QB is measured from North towards West. The formula is QB = 360° - WCB, or WCB = 360° - QB.
• Option 4 (N-W, QB = WCB 360°): The notation is ambiguous. If it means QB = 360° - WCB, it is correct for the N-W quadrant. However, given the structure and the confirmed correctness of statement 1, and the ambiguity of this option's notation, statement 1 is the most accurate and standard representation.

Based on the standard conversion formulas, statement 1 correctly represents the relationship for the S-W quadrant.