All right angles ARE equal, even if you bisect a circle. The angle between the curve and the line is defined to be the angle between the bisecting line and the tangent to the curve at the point of intersection. The subsequent right angles formed are all equal. No other definition of determining the angle between two lines (curved or straight) makes sense.
Your example of photocopying photocopies is not relevant. Photocopies are not perfect copies, so of course over time they will become more distorted from one another. Geometrical objects do not behave like this: they are perfect in that sense.