The whole circle bearing of a traverse are recorded as given below. Convert these to reduced bearings for BC & CD.

Line	AB	BC	CD	DA
bearing	70°30'	120°45'	223°30'	320°47'

Concept:

Whole circle bearing (WCB) system:

• All bearings are taken in a clockwise direction with respect to the North Pole.
• These bearings are observed by the prismatic compass.
• The whole circle bearing of any line varies from 0^∘ to 360^∘.
• The whole circle bearing is also called the azimuth.

Quadrantal bearing (QB) system:

• In this system, the bearing of the line is measured eastward or westward from the north or south pole whichever is near.
• These bearings are observed by the surveyor compass.
• It is also called reduced bearing system
• The quadrant bearing of a line cannot be greater than 90^∘.

RB of a line = WCB of a line (if 0^∘ < WCB < 90∘)

RB of a line = 180^∘ - WCB of a line (if 90∘ < WCB < 180∘)

RB of a line = WCB of a line - 180∘ (if 180∘ < WCB < 270∘)

RB of a line = 360∘ - WCB of a line (if 270∘ < WCB < 360∘)

RB = Reduced bearing, WCB = Whole circle bearing

Calculation:

Given

Calculating reduced bearing for BC:

Reduced bearing of line BC = 180^∘ - 120^∘ 45' = 59^∘ 15^∘ 

Reduced bearing of line BC = S 59∘ 15^∘ E

Similarly calculating reduced bearing for CD:

Reduced bearing of line CD = 223∘ 30' - 180∘ 0' = 43∘ 30∘ 

Reduced bearing of line CD = S 43∘ 30∘ W