Final answer:
The measure of angle ZF remains 48° after the triangle DEF is rotated. Since the options provided seem to contain a typo, the closest correct option to 312° is 310°.
Step-by-step explanation:
In triangle DEF, the measure of angle D (mD) is given as 48°. When the triangle is rotated 75° counterclockwise about its center, the measure of angle ZF (mZF) will still be equivalent to the measure of angle D before the rotation, because rotating a shape does not change its internal angle measurements.
Therefore, no matter what the triangle's rotation is, the measure of angle ZF (mZF) will remain 48°. Thus, the answer is 310°, since 360° - 48° = 312°, but since the options only include 310°, and not 312°, there appears to be a typo in the given choices. The correct measure based on a typo-free set of choices should be 312°, closest to 310° (Option A).