I'm going to assume that these are 45 degree angles, as that makes the whole thing a lot easier.
I see a few options. The simplest is to make the angles on a bigger piece first then rip off the edge banding. Use a board that is the same thickness as your divider material but decently wide (to allow easy handling). Tilt your table saw blade to 45, then position the fence so that the cut takes more than half of the thickness of the board off. Make one pass on each side of the board and you'll have a point centered on the thickness. Then put the blade back to 90 and position the fence so you're just taking off the strip you need on what is normally the "waste" side of the blade.
However, this isn't actually what I would do here. Gluing that tiny strip on will be an alignment nightmare, and you'll have to be really careful clamping it on to not damage the relatively fragile point. I would actually flip your assumption and glue on an oversize square edge banding first and then put the profile on the divider.
Start with stock thicker than the divider and wider than the point will need to be. Glue it on with overhang on both sides of the divider (I would recommend "bandy clamps" for this.) Then flush it up to the sides of the divider with a hand plane angled so the back of the sole is referencing on the divider's surface.
Now do the same as in the first paragraph, but sneak up the saw fence closer and closer until the cut lands as close as you need to the back edge of the banding.
Alternatively, if you don't have a table saw you can do this with a router table and a 45 degree bit. Use a miter gauge with a stop on it and sneak the stop up to where you need your cut to be the same way as you'd do with the fence above.
I also think you could do this pretty quickly with a hand plane. Just mark a line on the end of the banding at 45, extend the ends of the lines around the face and edge of the board, and then plane to the lines. If you're not comfortable with this at first do a couple trial runs on a piece of scrap. This also has the advantage that it will come out well even if your divider is a little warped (which will be a problem with the power tool methods.)