Try using "Points" with RandomInstance. For example:
GeometricScene[{a, b, c}, {Triangle[{a, b, c}],
PlanarAngle[{a, b, c}] == 30 \[Degree]}]
ri = RandomInstance[%]
ri["Points"]
(* {a -> {0.358567, -1.71279}, b -> {3.88163, 2.82286},
c -> {-1.92652, 0.457124}} *)