Identify given information and apply the tangent-chord theorem.

From the diagram, we are given that $DB = BE$ (indicated by the single tick marks).
Line AC is tangent to the circle at point B.
According to the tangent-chord theorem, the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

• For tangent BC and chord BE: $\angle CBE = \angle BDE$.
• For tangent BC and chord DB: $\angle DBC = \angle BED$.