Final answer:
The measure of angle EDF is 90 degrees.
Step-by-step explanation:
The measure of angle EDF can be determined using the properties of angles formed by a transversal cutting two parallel lines. Given that line EF is parallel to line DG, we can conclude that angle EDF is equal to angle DGF, since they are corresponding angles. Therefore, to find the measure of angle EDF, we need to determine the measure of angle DGF.
Angle DGF is formed by a transversal cutting lines EF and DG. We know that angle DGH is a right angle, given that line EF is parallel to line DG. Since angle DGH is a right angle and angle DGF is supplementary to angle DGH, we can conclude that angle DGF is also a right angle. Therefore, the measure of angle EDF is 90 degrees.