A bentech presentation......
Angle between plane and line

Use mouse pointer to have animations
You may also drag E
Use the Reset button to get position of the line  back

Reset

E: (2, 10, 5.5)
d: y(E)
c: x(E)
A: (2, 6, 3)
B: (-6.10076, 3.72603, 4)
C: (-6.10076, 8.31832, 4)
F = (4.136573433344481, 4.151390049683947, 0)
G = (6.6288846113171545, 3.1707690532718686, 0)
H = (7.366215677123961, 6.142384112847289, 0)
b = Plane(G, F, H)
a = Plane(A, b)
f = Line(A, E)
I: (2, 6, 5)
u = Vector(A, I)
D: (c, d, 3)
g = Segment(A, D)
J = Point(f)
K = Midpoint(g)
α = Angle(K, A, J)
β = Angle(J, A, I)