How to Compute the Average Angle
When observing an angle we take 4 readings, two in the direct and two in the reverse phase of the instrument. To compute the average angle, surveyors do it differently. Here is how to do it: Assume you are on point B observing points A and C to measure the angle ABC. You took the following readings
Direct to A: 10 5' 20"
Reverse to A: 190 5' 24"
Direct to C: 30 15' 32"
Reverse to C: 210 15' 38"
1- Compute the average readings: For each target, consider only one phase and do not change. Let us assume you will choose the direct phase. Take the degrees and minutes of that phase and the average of the seconds of the direct and reverse to a target as follows: Average reading to A: 10 5' 22" Average reading to C: 30 15' 35"
2- Compute the average angle by subtracting the average readings:
Angle ABC = 30 15' 35" - 10 5' 22" = 20 10' 13"
Notice that we do not compute two angles and take the averages, we compute the average readings and subtract them to compute the angle
You cannot keep the degrees and minutes of the direct phase for A, and then the reverse degrees and minutes for C. That is wrong. Either direct for both or reverse for both.
The avrage computed this way is considered one observation of the angle.
YOUR COMPUTATIONS FOR THE TRAVERSE PART AND ANY FOLLOWING ANGULAR MEASUREMENTS SHOULD BE DONE THIS WAY