Weird intersection or gap when I solidify I'm trying to make a pizza slice in Blender.  However, I'm having some trouble with this, as whenever I apply the solidify modifier, it goes from this to this.  It does a weird thing at the corner.  How to I prevent/fix this?
It looks to me like you don't have manifold(closed) geometry. you might have 2 vertices right on top of each other which makes it look like its manifold even though it isn't.

Try going into edit mode, hit A to select everything, then from the mesh menu select cleanup, and then merge by distance. you might have to play with the distance setting.