I'm working my way through the "surveyor reference manual" workbook (which is a little lacking in explanations) and I'm somewhat stumped on one of the questions. I assume that it wants me to find the back azimuth and then work from there adding interior angles etc... however it goes from adding 180° to later subtracting 180°. It seems like they are adding in extra steps with the 180° bit, but I'm not entirely sure what to make of it. I've included the question from the book and answer key below if anyone cares to help me out.
You can add the 180 if you want to. They are just getting the back azimuth, and in the instance of subtracting it keeps it between 0 and 360 without the additional step of subtracting 360 from a higher number (as they did in other parts). They are just trying to spin you around and see if you still make it back to the road.
For each leg you could apply a MOD 360 rule (modular) that may help clear it up for you. By that I mean if the calculated azimuth is greater than 360° then you subtract 360°, and if the azimuth is less than 0° then you add 360°. This only helps if I have understood your confusion correctly! Modular arithmetic
That looks like an Andrew Harbin survey problem.
James