Final answer:
The question seems to ask for a geometric angle calculation, but without further context or a diagram of the relationship between the angles EFW, ZWFG, and ZEFG, it's not possible to provide an accurate answer.
Step-by-step explanation:
To find the measure of angle mEFW, if given mZWFG = 138° and mZEFG = 166°, we would typically use the properties of the geometric figures involved. However, as the provided information does not explicitly describe the relationship between angles ZWFG, ZEFG, and EFW or the type of figure they are part of, it's not possible to give a definitive answer.
Usually, in a problem like this, if the angles were parts of known geometric figures such as triangles or polygons, we would apply the sum of angles in a triangle (180°) or the sum of interior angles in a polygon ((n-2)*180°, where n is the number of sides) to find the unknown angle.
Without further context or a diagram, we cannot proceed with a solution. Please provide additional geometric context or a diagram for further assistance.