The solution is correct. Size relative to circle is small. For illustrative purposes see the following.The points are plotted at bottom of circle. There is a fixed line as a reference and then gauge 'moves' (rotates line): note second point is around 0.03-0.04 radians.
pt1 = {-10680, -159610};
pt2 = {-5860.536872000001`, -159859.537514`};
Manipulate[Graphics[{Point[{pt1, pt2}], Circle[{0, 0},
Norm[pt1]], Line[{{0, 0}, pt1}],
Line[{{0, 0}, RotationMatrix[a].pt1}]}, AxesOrigin -> {0, 0},
Axes -> True],
{{a, 0}, 0, Pi/2, AngularGauge[##, GaugeLabels -> Automatic] &},
ControlPlacement -> Bottom]
