Final answer:
The question about parallel lines and angle measures cannot be answered due to insufficient information about the angle relationships and missing figures.
The correct answer is None of all.
Step-by-step explanation:
You have provided a question if EG and HJ are parallel lines and the measure of angle ∠JIF is 137°, what is the measure of which angle? Unfortunately the options (A) ∠D, (B) ∠E, (C) ∠G, (D) ∠K, are not defined in the context of your question.
To provide an accurate answer, I would need further information such as a figure or a description of how these angles relate to each other and to the given angles EG, HJ, and ∠JIF. With the current information, I am unable to determine the measure of the angles listed in the options.