Unfortunately the mouse method doesn't let you specify a specific rotation angle. You can hold down shift while you do the right click thing to constrain it to 15-degree increments, but this doesn't help if I want rotate something by 10 degrees.
Sure I can use the Layer - Rotate/Zoom option, but this only rotates the selection about the center of the picture. So, to use this method I'd need to select the region to rotate, move it to a new layer (so I don't obscure anything on my current layer), move it to the exact center of the image, then use that option to specify a rotation, then move it back to just the right spot, then merge it back into the other layer.
There doesn't seem to be a good way of rotating a selection a specified amount.
