Perhaps I don't understand the question. Angle of attack is a physical measurement, like crank angle or valve lift in the case of an engine. For instance, on fans with adjustable pitch, there is often an indicator near the adjustment or locking mechanism that shows the pitch angle of the blades. Some fan manufacturers also provide a device like a protractor that you put on the blade and read off the pitch. It sounds like you're wanting to measure something like "angle of separation" which would be a different thing altogether.

There is a "chord line" which connects the leading edge and trailing edge of airfoil. The angle between the far upstream flow velocity and chord is angle of attack.