In the end, after you inpired me (thank you all!!), here's what I did:

1) I duplicated both polygons

2) Used Boolean > Intersection so that I got a small piece which would serve as a "cap" for my corner, with the correct angle:



3) I then moved the end vertices from both polygons so that they would "hide" inside the cap:




4) And then got my final result:



I believe that's not the best way to do it. I guess I could perfect the end result by trimming the end of both polys using a copy of the cap for each one (then using Boolean > Difference), and then unite the three resulting objects.

But that worked for my needs....

Thank you all for your help.

Daniel