You are greatly overcomplicating this.
There is no need for polygon collision checks. Knowing your ticker's position (top of the wheel), and the rotation of the wedges, determine the one with the closest dot product. That's the one it intersects with.
To elaborate: think of wedges as arrows pointing outwards from the center of the wheel. An arrow's direction is a vector. So if a straight-up vector. Vector3.Dot will give you a value between -1 and 1, where -1 is 180 degrees and 1 is 0 degrees between the vectors, 0 is 90 degrees, etc.