Finding a branch isn't necessary. The tree trunk can be used as well, on any tree. Contrary to logic, it's possible to tie a hitch on a tree's trunk and it'll hold perfectly well against a vertical pull. Arborists use such setups routinely to catch very heavy logs from falling, and the forces there are far greater than what a human weighs.
Arborists usually use a running bowline, which they tie around the tree, and they also add an extra loop below it for added gripping power. But I have tested these kinds of setups, and any hitch can be used (e.g. an Anchor Hitch, or a Round Turn & Two Half Hitches). What's important is not whether it's a Running Bowline or something else, but rather that there are two loops around the tree. These setups work because the tree's rough surface creates enough friction and the rope doesn't slip. Even the extra loop below the main hitch isn't necessary (I have tried), but adding one has no drawbacks, only benefits.
This type of setup can be used on a tree's trunk, or on branches, regardless of their angle.
Videos with examples. The links open at the relevant times:
- A Running Bowline with an 'extra loop' around the tree below it:
- Another example of a Running Bowline with an 'extra loop' around the tree below it:
- A Running Bowline with an 'extra loop' around the tree above it. In this case, the whole setup is upside down, since he'll cut the tree at the bottom, so the rope will pull it upward: