Inner Product Notation

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I'm using a mathematics research paper to write code that calculates the minimum distance between two polygons. While I understand this isn't a code site, my questions is focused on how to read mathematical notation.

How do I interpert the angle between a point1 and line segment m = s(point2, point3) ? And the converse the the angle between line segment m = s(point2, point3)and a point1?

The values should range form -2*PI to 2*Pi

I'm first defining the angle_between(point1, point2, point3):

atan2(point3.y - point2.y, point3.x - point2.x) - atan2(point2.y - point1.y, point2.x - point1.x
  1. So in this paper, is alpha_double_prime:

    angle_between(m(p), m(q),e(i)) OR the opposite angle_between(m(q), m(p),e(i))

  2. In this paper, is beta_double_prime equal to:

    angle_between(m(p), m(q),f(j-1)) OR the opposite angle_between(m(q), m(p),f(j-1))

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Polygon

Paper referenced