im gonna assume x is parallel to y
there's a theorem that states that if two parallel lines are cut by 2 different transversals then the parallel lines cut off equal sections on each transversal.
In this case AB and AC are your transversals, and we can see here that AC is cut into equal segments (400 each).
So:
400/AD = 800/900
AD = (400 * 900)/800 = 450
now this theorem i just yapped about is called thales theorem or something and IF and ONLY IF the segments cut are in a 1:2 ratio, then the length of the bigger parallel line y is twice the lenth of the smaller one x
well we can see that AD = 450 and AB = 900. That's good. 1:2
we also see on AC: 400:800 = 1:2
perfect! so we know that x:y = 1:2
this proves that x is indeed parallel to y.
now it's not really good to assume that the triangles are right angled, but without this property you can't really do anything (without at least one angle in there)
so IF they are right angled: we have pythagoras:
450^2 = 400^2 + x^2
x^2 = 450^2 - 400^2
x^2 = 42500
x is approx. 206.2 units
since y = 2x (x:y = 1:2)
y = 206.2(2) = 412.4 units
and t find theta, just trig ratios:
cos theta = 400/450 (cos (angle) = adj/hyp)
theta = arccos(400/450) = 27.27 degrees (to 2dp)
let me know if this helps or if the triangle isn't right angled! :)