Glossary of angles in solid geometry

Geometry Level 4

In a 3D Euclidean space, there is a tetrahedron V A B C V-ABC where A B C \triangle ABC is equilateral and V A = V B = V C VA=VB=VC , P P is a point on edge V A VA (not including point V V and A A ).

Angle α \alpha denotes the acute angle of the line P B PB and A C AC , β \beta denotes the angle of P B PB and plane A B C ABC , and γ \gamma denotes the dihedral angle P A C B P-AC-B .

Which of the following is true ?

Show your rigorous proof.

β < γ , α < γ \beta<\gamma,\ \alpha<\gamma α < β , γ < β \alpha<\beta,\ \gamma<\beta β < α , γ < α \beta<\alpha,\ \gamma<\alpha β < α , β < γ \beta<\alpha,\ \beta<\gamma

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