Measure and Construction cannot be accused of being intuitive to use, but once you can use it, it is actually quite helpful, and can do what you are asking for IF your models meet its requirements, which are, basically, that your meshes are editable poly objects, and that you set it up carefully enough.
The procedure is as follows:
1. Prep - make sure your meshes are editable, and have their axes in the correct place for rotation.
2. Activate point snapping. The Tool itself should auto-snap even without this, but this aspect of it is flaky, so rely on proper snap instead !
3. Get M&C Tool from Tools / Guide / M&C. A red line should appear arbitrarily placed in viewport.
4. Drag the start of the red arrow to the nearest vertex to your intended hinge point, then the end of it to an equivalent point at the end of the object.
5. Hold control and click again to establish a second measure (green line), and snap / align that relative to the first.
At this point the angle between the 2 should be displayed and selectable for editing simply by changing the rotation value in the M&C attributes. Here is a quick video in which I attempt to demonstrate that...
MandC Wrangling.mp4
CBR