I'm not sure what all that extra stuff is supposed to mean, but the answer to the top question is: x = -6
Step-by-step explanation:
δabc ≅ δdcb by sas because
db ≅ ac . . given (side)
bc ≅ bc . . reflexive property (side)
∠dbc ≅ ∠acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)