This is a workaround which can be used in case you are later going to rotate something else as much.
An imaginary example:
The boss says that the next artwork is otherwise good, but the black shape should be rotated around point A until it looks right. He stands behind my back and he will say, when it's right. Then the green shape should be rotated exactly as much around point B. The artwork:
To see how much the black shape is rotated I draw a horizontal reference line (blue) which starts from A. Then I select the line and the black shape simultaneously, enter into the rotation mode and move the rotation center to A. One must have all point snaps =ON to make the rotation center to snap to the wanted point:
Let's assume this is the position worth money for the black shape:
The next step is to apply Object to Guide to the reference line and move the new guide line to point B. I draw also a new reference line starting from B (orange):
I select the orange reference line and the green shape, move their rotation center to B and rotate until I get an indication of the snapping to guide from the endpoint of the orange line. The rotation is completed:
Beware: Snap to bounding box is harmful. Keep it OFF.