Corner of path tapering to a point
I'm trying to learn Illustrator so I'm sure this is a basic question, but I can't figure it out. I have a curved path that abruptly changes direction at one point. If angle of the corner that creates is large enough, the corner of the path tapers to a point like I want. If it's ever so slightly smaller, the corner is blocky. Please see animated gif:

Note how the path on the left has a nice point at the corner, and the path on the right looks chopped off. Is there any way to get the path on the left to taper the same way?
