The correct answer is C) the plane of the observer's meridian. At meridian transit, the diagram used by a navigator to illustrate the angles involved is based on the plane of the observer's meridian. This is because the meridian transit occurs when a celestial body, such as the sun, crosses the observer's local meridian, which is the north-south line that passes directly overhead. The other options are incorrect because they do not accurately represent the frame of reference used in the meridian transit diagram. Option A and D refer to the celestial equator as observed from the north and south celestial poles, respectively, which are not directly relevant to the observer's local meridian. Option B refers to the plane of the Greenwich meridian, which is not the same as the observer's local meridian.