Final answer:
The question lacks sufficient detail to provide a specific measure for the angle in question as it does not state the value of ∠EDH or ∠EDG or their relationship to the rest of the circle.
Step-by-step explanation:
The question presented is not completely clear as it's missing specific information regarding the diagram or the values of angles ∠EDH or ∠EDG.
However, given that the two angles are congruent, we understand that their measures are identical. Without further details, we cannot provide a precise answer to the measure of the angle being asked for.
Generally, the measures in a circle add up to 360 degrees, and if ∠EDH ≅ ∠EDG in circle D, we'd need to know the rest of the context or the measure of one of these angles to determine any other angle's measure within the circle.