1. **Problem:** Find the measure of angle $\angle D$ in the parallelogram $DEFG$ where side $DG = 3.6$ ft, side $GF = 8$ ft, and $\angle F = 106^\circ$. 2. **Formula and rules:** In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum to $180^\circ$). 3. Since $\angle F = 106^\circ$, the adjacent angle $\angle G$ satisfies: $$\angle F + \angle G = 180^\circ$$ $$106^\circ + \angle G = 180^\circ$$ $$\angle G = 180^\circ - 106^\circ = 74^\circ$$ 4. Opposite angles are equal, so: $$\angle D = \angle F = 106^\circ$$ **Final answer:** $$m\angle D = 106^\circ$$