If the quadrantal bearing of a line is S 36° 30’ W, then the whole circle bearing of the line is
- A190° 30’
- B170° 30’
- C350° 30’
- D216° 30’Correct
Solution
Concept
Quadrantal bearing to whole circle bearing conversion
Formula
WCB = 180 + QB
Step-by-step solution
1. Quadrantal bearing S 36° 30’ W lies in the third quadrant (South-West quadrant). 2. To convert a South-West quadrantal bearing to Whole Circle Bearing (WCB), add 180° to the quadrantal bearing angle. 3. WCB = 180° + 36° 30’ = 216° 30’. Answer: D
Explanation
A quadrantal bearing of S 36° 30' W lies in the third quadrant, which is measured clockwise from the South axis toward the West. To convert a South-West bearing to a whole circle bearing measured from North, 180 degrees must be added to the quadrantal angle. Adding 180 degrees to 36 degrees 30 minutes gives a whole circle bearing of 216 degrees 30 minutes.
Why the other options are wrong
A) 190° 30’ is incorrect because S 36° 30’ W corresponds to 180° + 36° 30’ = 216° 30’. B) 170° 30’ corresponds to an angle in the second quadrant. C) 350° 30’ corresponds to an angle in the fourth quadrant.
Shortcut
South-West quadrant (S-W): Whole Circle Bearing = 180° + Quadrantal Bearing.
Common mistake
Incorrectly subtracting the angle from 180° instead of adding 180° to convert SW quadrant bearing to whole circle bearing.
Correct answer: D) 216° 30’