To determine the measure of angle FEH, I would need more context or information, such as a diagram or description of the relationships between points F, E, and H. Without that, I cannot accurately provide the measure of angle FEH or confirm any of the options (134 degrees, 180 degrees, 44 degrees, or 54 degrees).
If you have any additional details or descriptions, please share them, and I'll do my best to help you!