How to calculate angle of rotation based on XY coordinates?

If you have the X and Y of each border, then you have the X and Y of each of the four lines that makes up the square.

So working out the angle is easy: school level geometry.
Take one of the angles - the top right in your example.
You know the coordinates of the line that is part of the square: P1, and P2, so you know the difference in X coordinates: P2.X - P1.X
That allows you to make a right angle triangle, where you know the Hypotenuse (from Pythagoras on P1 and P2) and Adjacent line lengths ( the difference in X co-ords).
So you can work out the angle simply:

Theta = Cos^-1(A/H)

You covered all this in Maths class when you were what? 12? :laugh:

This works perfectly for me

const double Rad2Deg = 180.0 / Math.PI;
const double Deg2Rad = Math.PI / 180.0;

/// <summary>
/// Calculates angle in radians between two points and x-axis.
/// </summary>
private double Angle(Point start, Point end)
{
    return Math.Atan2(start.Y - end.Y, end.X - start.X) * Rad2Deg;
}