1. **State the problem:** We need to find the measure of angle $\angle DG$. 2. **Identify the context:** Since the problem only states $m\angle DG$, it implies we are looking for the measure of angle at point $G$ formed by points $D$ and $G$. 3. **Assumptions:** Without additional information such as a diagram, coordinates, or other angle measures, we cannot calculate $m\angle DG$ directly. 4. **Request for more information:** To solve for $m\angle DG$, please provide a diagram, coordinates of points $D$ and $G$, or other related angle or side measures. Since the problem lacks sufficient data, no calculation can be performed at this time.