Split a curve where the changes angles

I have a bunch of curves like this

that I want to be two different curves that meet at the endpoints.

I am struggling to find a way to do this.

The component Explode should do it
(Curves > Utilities > Explode)

Easy and probably what you need. But you can also use the Shatter component and provide a set of splitting parameters. You can create parameters at kinks and other discontinuities using the Discontinuity component.