Adjusted angles and bearings, angles to the left

The traverse starts on the known line AW and ends on the known line DX, so the observed angles can be checked and adjusted.

Rule for angles measured to the left (counter-clockwise from the back line to the forward line):

$$\text{Bearing of forward line} = \text{Bearing of back line} - \text{angle to the left}$$

where the back line is the line from the station towards the previous station. The back line at the next station is the forward line $\pm 180^\circ$.

Step 1: Compute the bearings from the observed angles

Step 2: Angular misclosure

Known bearing of DX = 358° 18.5′; computed = 358° 17.7′.

$$\text{Misclosure} = 358^\circ 18.5' - 358^\circ 17.7' = +0.8'$$

To raise the computed bearing by 0.8′, the angles to the left must be reduced. There are 4 angles, so the correction is $-0.8'/4 = -0.2'$ per angle.

Step 3: Adjusted angles and bearings

Check: the bearing of DX obtained from the adjusted angles equals the known 358° 18.5′.

Answer: adjusted angles A = 208° 07.4′, B = 101° 34.9′, C = 89° 05.1′, D = 17° 11.7′; adjusted bearings AB = 26° 10.2′, BC = 104° 35.3′, CD = 195° 30.2′, DX = 358° 18.5′.