The correct answer is A) 112.5°. The reasoning is that a vessel heading ESE (East-Southeast) is traveling on a course of 112.5°. This is because the cardinal directions (N, E, S, W) are spaced 90 degrees apart, and the inter-cardinal directions (NE, SE, SW, NW) are spaced 45 degrees apart. Therefore, ESE is 45 degrees between East (90°) and Southeast (135°), which equates to 112.5°. The other options are incorrect because B) 135.0° is the course for a vessel heading SE, C) 157.5° is the course for a vessel heading SSE, and D) 180.0° is the course for a vessel heading South.