How to cut the correct angle on transition strips

Firstly, note that the cuts on two adjoining pieces should have the same angle, but in the opposite direction. Failure to do this will result in something like you've shown us here, with points sticking out and part of the cut end exposed. That's just not good at all.

Secondly, each joint should pass exactly over the corner in the flooring. This doesn't tell you anything about the length of your pieces, but it helps tell you whether you're on the right track when working out fitment.

Thirdly, always cut a bit long. You can easily re-cut the same angle if needed, and you can adjust if needed. You can't cut a board longer.

If you started with a 45 degree clip in your flooring then it's simple. Each bend is 45 degrees (half a 90), so each cut is half that, or 22-1/2 degrees. Since there's a bit of play in where you install the moldings, this should work fine and give you nice tight miters. Set all pieces in place, adjust positions slightly to get a perfect fit, and lightly trace the position on your flooring as a guide for the final install.

If you don't know or the angles aren't 45 degrees you have a couple options. You can use a carpenter's square or bevel gauge to measure the flooring angles, then simply divide each in half.

Another technique is to lay two pieces in place, overlapping each other at the miter. Precisely mark the point on each edge (inside the bend and outside) where the two pieces intersect. Now when you go back to your miter saw you have two points to cut along.

Or you can use trial-and-error and some scrap wood. Width doesn't really matter. Start with two cuts at 22-1/2 degrees. Set the scraps against the flooring and see what's what. Adjust the cuts (always cut both pieces to the same angle!) in small increments until it's just right, then cut your molding.

One last tip: Use wood glue in the miters. Hold them in place with masking tape to the wood floor, pulling it all inward. Wipe any squeeze-out off and clean up with a damp cloth. A couple hours should do. This will help keep them from working open and will serve to mask any slight angle issues.