x=130

Explanation:

In triangle ACD,

∠3 = ∠1 + ∠C __________________ (i)

In triangle ABD,

∠4 = ∠2 + ∠B __________________ (ii)

Adding equation (i) and (ii),

∠3 + ∠4 = ∠1 + ∠C + ∠2 + ∠B

⇒ ∠BDC = (∠1 + ∠2) + ∠C + ∠B

⇒ x°= 55°+ 30°+ 45°

⇒ x°= 130°