See the following image :

Suppose the robot starts at A and moves 10m North to B......he then turns 44° to the right and moves anonther 10m to D......at D he turns 55° to the right and moves 10 more meters to F.....he then turns x degrees and faces due South (along FG)
If we connect BF ....note that angle BDF = 180 - 55 = 125°
Since BD = DF....the angles DBF and DFB must be equal.....so the measure of angle DFB = [ 180 - 125] / 2 =
55/2 = 27.5°
And angle FBG = 90 - CBD - DBF = 90 - 44 - 27.5 = 18.5°
And triangle BFG is right with angle BGF = 90°
So angle BFG = 90 - FBG = 90 - 18.5 = 71.5°
So angles DFB + BFG + HFG = 180
So 27.5 + 71.5 + HFG = 180
99 + HFG = 180
HFG = 180 - 99 = 81° = x = the number of degrees in the last turn
