Angles in pentahedron (oblique pyramid)

Question

I have an arbitrary pentahedron (quadrangular oblique pyramid). I want to compute of the angle $\delta$ of the figure provided that the angles $\alpha$, $\beta$ and $\gamma$ are known, along with points $P_1$ and $P_2$.

Answer 1

Without additional constraints imposed on the polyhedron's geometry, it is obviously not possible to establish such a relationship for the sum of the face angles incident to the apex, since as the distance between the apex and the base increases to infinity, the sum of these angles will tend to $0$; conversely, as the apex approaches the base, the sum tends to $2\pi$.