A student says that the measures of coterminal angles are never opposites of each other. Is the student correct? Explain.

Answer:

The student is incorrect. For two angles to be coterminal, the difference between their measures must be a multiple of 360°. If we consider the measures 180° and -180°, these two values are opposites of each other. The difference between them is 180° - (-180°) = 360°, which is a multiple of 360°. Therefore, 180° and -180° are coterminal angles that are opposites, proving the student's statement is false.