If lines AB and CD intersect as shown below, the value of angle x = ?

In Δ EBC :
∠EBC = 30°
∠BCE = 125°

Now all angles of triangle add up to 180 degrees

So ∠BEC + ∠ECB +∠EBC = 180°
∠BEC + 125° + 30° = 180°
∠BEC + 155° = 180°
∠BEC = 180° - 155°
∠BEC = 25°
 
Now ∠BEC = ∠DEA (They are vertically opposite angles)

In Δ ADE:
∠ADE = x
∠DAE = 25°
∠DEA = 25°

∠x + ∠DAE + ∠DEA = 180°
∠x + 25° + 25° = 180°
∠x + 50° = 180°
∠x = 180° - 50°
∠x = 130°