You probably need to rotate the Pivot of the blue surface to align with the “hinge” edge.
Rotating the Pivot can be tricky, since it doesn’t tend to do what you expect when trying to rotate from perspective view. Hint: After each failed attempt, re-run the command and check “Reset” to get back to a reasonable starting point.
After starting the command, and when picking a first reference point, pick one of the World axes (X, Y or Z), and then for the second reference point, use a view which is “axis aligned” with your geometry (perhaps a CPlane in your case, or rotate the geometry to align the “hinge edge” with the World axes), and finally pick the reference point from a corner of the surface you want to rotate.
As said, rotating the pivot this can be tricky until you figure out its behaviour, and the problematic bit is mostly due to the fact that rotating the Pivot typically doesn’t work well if trying to do it from the perspective view (it tends to rotate only in one axis at the time, hence it is easier to rotate if first aligning either a CPlane to the geometry, or the geometry to some plane axis, before trying to rotate the Pivot). Efter the Pivot is properly rotated/aligned, rotate the geometry back to it’s original orientation.
The Rotate pivot button is, typical for Bongo, hidden from you to be visible only when the Bongo properties panel is visible, and looks like this:

It may be easier to start the command via the command line (_BongoRotatePivot) or via the Bongo menu (in the menu it is always available if you start by right-clicking on the Bongo Panel/Navigator):
So the key issue is to rotate the Bongo Pivot one axis at the time, but If not one axis at the time, then the rotation will most probably not end up in the desired (correct) direction.
Finally define the Hinge to rotate around the (aligned Pivot) axis of your choice.
// Rolf