the standard for measuring angles is counterclockwise from the +x axis.
the angle marked for the pole at the origin, s1, is measured that way.
the blue line you added at that pole is not the correct way to measure the angle.
the pole at -1 -j is measured correctly - counterclockwise from the +x axis
since the start is not at the origin, we treat it as is the start is at the origin
the other poles and zeros on the x axis are alos measured that way -
since they are not at the origin, we treat it as if the origin was at the start
of the vector, measure counterclockwise from the +x axis
the angle theta for the pole at -1+j is also measured correctly,
using the same CCW from + x axis
i take it from your blue additions that "inner" means the acute angle
so that at the origin, the obtuse (outer?) angle is CCW from +x axis
and the acute angle (inner?) is CW from the -x axis
for those raised on digital clocks, counterclockwise is the direction
of rotating the +x axis about the origin toward the +y axis
and clockwise is the other rotational direction