The correct answer is B) 135.0°. The compass course of a vessel heading southeast (SE) is 135.0°. This is because southeast is one of the four cardinal directions on the compass, and each cardinal direction corresponds to a specific compass bearing of 45°, 135°, 225°, or 315°. Since southeast is the midpoint between south (180°) and east (90°), the compass course for a vessel heading southeast is 135.0°. The other answer choices are incorrect because: A) 112.5° is the bearing for east-southeast (ESE), C) 157.5° is the bearing for south-southeast (SSE), and D) 180.0° is the bearing for south, which is not the same as southeast.