EDIT: My first idea didn’t work…this one does:
Here are your two vectors
- TURN OFF SNAP TO GRID
- Rotate the vectors (or a copy of them) so that one leg rests along a grid line
- Then Draw a box smaller than the vector bounding area
- Drag the box’s lower left corner so it snaps onto the vertex of the vectors
- Scale the rectangle using the top-middle handle until the top-right handle lines up with the second vector
- Hit Done.
- The rectangle is still selected so the width and height values shown on the screen are the numbers you need
The angle is arc-tangent of (the Height of the rectangle divided by the width)
atan(h/w)
In this case: 52.866691379636990706376552930063 degrees 