I do feel your pain about vetting "professionals", especially living in a place that tries to prevent me from making my own improvements.
See: https://www.structuralbasics.com/rafter-roof-design/ and imagine how you would get a rectangular piece of wood for the rafter to sit flush against the rectangular joists/beams.
The roof structure is built by carpenters or framers. Or more likely just delivered as pre-built trusses which are placed on top of the walls.
For a roof built on-site, a speed-square or framing square will include markings for common roofing cuts, hip/valley cuts, etc. You have to know how to use them but you don't really need to understand the underlying trigonometry.