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Step-by-step explanation:

The base angles of each isosceles triangle are congruent. So ∠ABD = ∠BAD = 36°. The exterior angle BDC is the sum of the remote interior angles BAD and ABD, so is 36°+36° = 72°. Angle DCB is congruent to that, so is 72°.

Angle BDA is the supplement of angle BDC, so is ...

  ∠BDA = 180° -72° = 108°

Angle DBC can be computed a couple of ways. One is to make use of the relationship to exterior angle BDA:

  ∠DCB +∠DBC = ∠BDA

  ∠DBC = 108° -72° = 36°

In summary, ...