I'd like to confirm a couple of points.
1) the max angle feature was designed to and should only be removing EXTERIOR triangles. If you have a data set that shows otherwise please submit it on a service ticket.
2) this feature should be respecting exterior breaklines/feature lines/ survey features and is the subject of a defect I recently submitted.
Everything seems pretty wrapped up, however I would like to add that I find just adding an outer boundary is the simplest way of making sure the generated surface stays within the available data set, and doesn't triangulate between points where it shouldn't. As mentioned above, when when adding additional data, the boundary can be moved down in the build list so it's added last.
Whereas when deleting lines, after a lot of deletions and manipulations its quite hard to keep track as to which line was where; this became a problem for me before when I deleted lines and then had to add additional data to the surface because some of the triangulation wasn't working out correctly because of the deleted lines.
Here is a post that I started, where a comment from El_nath seems to indicate that the Maximum angle option was introduced for the purpose of being able to add the boundary of one surface to be hide boundary on another surface. This was disigned to work with corridor surfaces so you could hide the portion of the EG surface where the corridor is - I don't believe it was originally designed to work with survey surfaces.
I have recently tried out the maximum triagle option and it is still not perfect. As the attachements show there are still a couple of holes in the surface and it ignores some breakline segments. But I still beleive it is a big improvement on where it was when first introduced, and if it does not work perfectly it can still be used to create a boundary that is almost there and then just needs a couple of edits.
The max angle option was added to clean up the triangles at the edge of any surface. For the corridor surfaces, typically those are pretty clean already because feature lines are used to generate the boundary.
IMO, the only way of doing it simply and reliably is with outer or dataclip boundaries, as either polylines or feature lines, and then be careful as to the placing of the boundary in the definition list.
Delete lines are fine for very minor or temporary edits but you'll get plenty of triangles re-appearing later if you end up performing more functions or edits on the surface. And then good luck finding the edits you need to reinstate or delete.