1. **Problem statement:** We are given a triangle with vertices A, B, C, and a point D on the baseline from A to D. The angle at vertex B is $128^\circ$. We need to calculate the size of angle $BCD$. 2. **Given information:** - $\angle ABC = 128^\circ$ - Point D lies on the baseline from A to D. - The angle at C between lines DC and BD is approximately $35^\circ$ (from the protractor). 3. **Understanding the problem:** Since $D$ lies on the baseline and the protractor measures the angle at $C$ between $DC$ and $BD$, we want to find $\angle BCD$. 4. **Using the fact that the sum of angles around point C on a straight line is $180^\circ$:** If $\angle BCD$ is the angle between $DC$ and $BD$, and the protractor shows approximately $35^\circ$, then $$\angle BCD \approx 35^\circ$$ 5. **Conclusion:** The size of angle $BCD$ is approximately $35^\circ$ based on the protractor measurement. **Final answer:** $$\boxed{35^\circ}$$