1. **Problem statement:** We have a quadrilateral ABCD with diagonal BD splitting it into two triangles ABD and BCD. 2. Given: $\angle CBD = 60^\circ$ and right angles at vertices C and B. 3. Since $\angle C$ and $\angle B$ are right angles, triangle BCD is a right triangle with $\angle C = 90^\circ$. 4. In triangle BCD, the sum of angles is $180^\circ$. So, $$\angle BDC = 180^\circ - \angle CBD - \angle C = 180^\circ - 60^\circ - 90^\circ = 30^\circ.$$