1. **State the problem:** Given that $m\angle ADC = 180^\circ$ and $m\angle ADB = 152^\circ$, find $m\angle BDC$ in degrees. 2. **Understand the setup:** Since $m\angle ADC = 180^\circ$, points A, D, and C are collinear with D between A and C, forming a straight line. 3. **Use the angle addition rule:** The angles around point D on the straight line add up to $180^\circ$. The angle $\angle ADC$ is a straight angle, so the sum of angles $\angle ADB$ and $\angle BDC$ must equal $\angle ADC$. 4. **Write the equation:** $$m\angle ADB + m\angle BDC = m\angle ADC$$ 5. **Substitute known values:** $$152^\circ + m\angle BDC = 180^\circ$$ 6. **Solve for $m\angle BDC$:** $$m\angle BDC = 180^\circ - 152^\circ = 28^\circ$$ **Final answer:** $$m\angle BDC = 28^\circ$$