The node editor that @Gaffboat suggested it the easy way to do it with your artwork…
Both object have to be closed for the boolean assistant to work…
You will have to close the wiggly line.
Besides auto join selected shapes, there are a couple of options to help close shapes and close shape with tolerance. They may work for you… I’m never tried with your type of artwork.
I used Select open shapes in the Edit menu.
If I use close open shapes with tolerance and increase the tolerance enough…
When I select both, I have the boolean options. This may not give you the results you want…
Using ^B (control+B) will display the boolean assistant. Hovering over the node editor icon will display the edit tools for node edit.
Good luck
