Which of the following statements best describes two $\mathrm{coterminal}$ angles?

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

Answer: (B)

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 because coterminal angles share the same terminal side, they lie along the same ray from the origin, but they may be located in different rotations around the circle.
4. Note that coterminal angles are not necessarily in the same quadrant because adding or subtracting full rotations can place the angle in different positions, but the terminal side remains the same.
5. Conclude that the best description is: 'They have the same initial side and the same terminal side but may have different measures.'