Hi,
any suggestions, on how to properly connect such open corners? I have painstakingly opened them, removing false creases from the corner, and not I would need to find the intersection points of polylines.

The extension lengths are arbitrary and the angles are arbitrary. Curves are planar and on XY.
The pic posted is a simpler case. There are hundreds of different ones.

@HS_Kim
Thank you, this did the trick! The curves were already sorted as they were once one polyline, so I could just take the shift-intersection part.

@Joseph_Oster@Japhy Sorry, about the lack of geometry. It was the end of the day cry for help.
I could explain a bit about the big picture here. This part is related to my work on massive timber plate fabrication (CLT, LVL) and automated toolpath generation from IFC model to Hundegger machine using BVX file format.

The issue is that I need the geometric outline of each piece (basically TOP view footprint), which is easy if the edges are perpendicular. But once you have to tilted edges meeting, then the part outline is not sufficient in generating correct geometry.
This is one case.