Give this a try :
* make sure the object global rotation is reset
* select the edge, set transfrom modes to COG & Global, then set rotation Z to the nearest 90 step (-180, -90,...), same after that for Y. X won't work well because it's rotating around the edge itself
* if you want to rotate the whole connected island around the edge, set proportional second curve point to value 1, increase distance to 100, and check "consider neighborhood" (for rotating the whole model, uncheck it)
* if you want only some of the polygons, disconnect them before the rotation, and delete the disconnect operator from the stack afterwards.
(doh realized this is probably uv related as you mentioned a uv tutotial
.. yes this would require a script. Unless you use a plugin like "UV Edit by Mesh" this might work with the workflow above, but might be overcomplicated because you would have to move the parts that you don't want to move out of the influence of proportionlal, then move them back..)