There’s no need to model the panels with thickness to merely find the miter angles and lengths.
Simply model the exterior Faces only.
There is a (free) plugin which will yield the dihedral angle.
The miter angle = the dihedral angle / 2
Angle Between Planes v1.0 — SketchUp plugin by Clark Bremner
Read the plugin documentation and then experiment with it.
http://sketchucation.com/forums/viewtopic.php?p=137656#p137656
Here’s what it does.
Right click on the common edge of two faces.
The dihedral angle is immediately displayed in the context menu.
