90 degree angle in air conditioning ducts, should I avoid them?
The reason that 90 degree turns (or any tight radius bends) in duct systems are discouraged are because they reduce air-flow. The friction that is encountered by the moving air as it hits the wall of the turn slows it down decreasing the distance it can travel.   There are equations that can be used to calculate the number of bends  before air performance is affected. Duct size and shape, motor wattage, register opening, etc. will need to be considered. If you can orient the duct system and configure the shape with "gentler" turns such as using (2) 45 degree bends in place of (1) 90 degree bend. This would restrict air-flow less. Installing a motorized fan duct in-line with the new duct branch would allow for longer runs if needed and account for sharp turns.    Is it feasible, when viewing the drawing you posted, to branch off the main duct sooner with a 45 degree duct and circumvent the restroom with 45's? Or consider using flexible insulated duct which is much more bendable than stamped sheet metal ducting. I'm not positive that code will accept this type of configuration ( rigid to flex back to rigid), but someone should comment about it either way).