1. **Problem statement:** Find the measure of angle $\angle CDE$ in the given circle with center $G$ (or $A$ as described), where $CD$ is a diameter and angles at the center are given as $28^\circ$ and $77^\circ$. 2. **Key fact:** The angle subtended by a diameter on the circle is a right angle, so $\angle CDE = 90^\circ$ if $CD$ is a diameter. 3. **Given:** $CD$ is a diameter, so $\angle CDE$ is an inscribed angle subtending the diameter. 4. **Therefore:** By the Thales' theorem, $\angle CDE = 90^\circ$. 5. **Additional info:** The angles $28^\circ$ and $77^\circ$ at the center help confirm the positions but do not change the fact that $\angle CDE$ is a right angle. **Final answer:** $$\boxed{90^\circ}$$