We have a vector that which location is true bearing of 140°.
We have to express the quadrant bearing.
True bearing is a directional measurement where the angle is measured clockwise from North.
We can graph this vector as:
Then, as the vector is close to the South direction, we measure the angle of the vector from the South direction. in this case, the angle goes to the East.
The angle has to complete 180° between S and N, so the angle for the quadrant bearing is 180-140 = 40°.
We then can express the quadrant bearing as: S 40° E.
NOTE: if the vector was closest to the N, we should have used the N direction to measure the quadrant bearing, to the East or to the West depending on the vector.
Answer: S 40° E.