BD = CD

∴∠CBD = ∠BCD = 30°

In triangle BCD,

∠BDC + ∠BCD + ∠CBD = 180°[Sum of angles of triangle]

⇒ ∠BDC + 30° + 30° = 180°

⇒ ∠BDC + 60° = 180°

⇒ ∠BDC = 120°

Now,

∠BDC + ∠BAC = 180°[ABCD is a cyclic quadrilateral]

⇒ 120° + ∠BAC = 180°

⇒ ∠BAC = 60°