Can somebody explain how all three of these deflection angles are to the right? Angle C is the only one that makes sense to me that it would be to the right.
I'm having a hard time understanding the question. If you traverse clockwise around a parcel or project, your angles will always be interior and angle right.
From what I see in the clipped image, you'll need to leave the idea of a deflection angle out. If you are thinking of the angles as deflection angles, you may be trying to extend the preceding line and then to get to the forward line you would need to turn left for A and C (but not using the angles shown; instead 180-'the shown angle'). But that is not what is given. I hope that particular image was not in a section called deflection angles.
You are provided the observed angles at these points and are provided the statement of them being to the right. In this case, the instrument would be sighted along the back line and turned to the right until sighting along the forward line.
Many old descriptions were written such that the direction of the next call was listed as being a specific angle relative to the back site. Other scriviners preferred to call out a specific angle relative to the fore site. That is: one case might say, thence on an angle bearing 120 degrees to the right while in another case the scriviner would say, thence deflecting 60 degrees to the left. It would be the same line, yet described in a different manner.
How does a description come before closing a traverse, balancing it and applying the results before making a resolution writing a description?
The angles can be expressed various ways and, if consistent, be understood.
What annoys me is that before GNSS, angles were measured but then the parcel map showed bearings. Then for retracement the bearings had to be turned back into angles. Too much chance for blunder, especially when this wasn't computerized.
Back in the day we balanced our angles, converted to azimuth, reduced to lats and deps, adjusted, then broke the triangles to derive bearings. Putting it back to angles would have added a step...