Which of the following statements best describes two coterminal angles?

• A. They are always $\mathrm{complementary}$ angles.
• B. They are always $\mathrm{supplementary}$ angles.
• C. They always have the same measure and are in the same quadrant.
• D. They have the same initial side and the same terminal side but may have different measures.

Answer: (D)

Verified step by step guidance

1. Understand the definition of coterminal angles: Coterminal angles are angles that share the same initial side and the same terminal side when drawn in standard position on the coordinate plane.
2. Recall that coterminal angles can differ by full rotations of 360 degrees (or \$2\pi$ radians), meaning their measures are not necessarily the same but differ by multiples of 360 degrees.
3. Recognize that complementary angles sum to 90 degrees and supplementary angles sum to 180 degrees, which is unrelated to the concept of coterminal angles.
4. Note that coterminal angles may lie in different quadrants depending on their measure, so they do not always have the same measure or lie in the same quadrant.
5. Conclude that the best description of coterminal angles is that they have the same initial and terminal sides but may have different angle measures.