# Including all constraints in a geometry problem

I'm trying to solve this geometry problem using GeometricScene:

Find angle x:

Here's my (incomplete) code:

scene = GeometricScene[{{a, b, c, d, e, f}, {x}}, {GeometricAssertion[
Triangle[{a, b, c}], "Counterclockwise"],
GeometricAssertion[Triangle[{a, d, c}], "Counterclockwise"],
GeometricAssertion[Line[{b, c}], "Horizontal"],
Line[{b, e}],
Line[{e, d}],
PlanarAngle[{b, a, d}] == \[Alpha],
PlanarAngle[{d, a, c}] == 2 \[Alpha],
PlanarAngle[{e, b, c}] == \[Beta],
PlanarAngle[{e, b, a}] == 2 \[Beta],
CollinearPoints[{b, f, e}],
CollinearPoints[{a, f, c}]
(* PlanarAngle[{a,d,e}]== 2 \[Phi],*)
}];
RandomInstance[scene]


As I've done in similar problems, I build up the constraints one by one, seeing the RandomInstance become more and more constrained. Once I get all the constraints imposed, I use:

Replace[x, %["Quantities"]]


to compute x.

All works fine until I try to impose

PlanarAngle[{a,d,e}]== 2 \[Phi]


which Mathematica will not then render. (I don't even try adding the remaining constraints.)

I believe I've defined sufficient elements and constraints up to the stated condition.

How can I add all the required constraints and thereby solve this geometry problem?

Incidentally: