In the context of angles in standard position on the coordinate plane, which of the following pairs of angles are called coterminal angles?

• A. Angles that have the same initial side and the same terminal side, such as $30°$ and $390°$
• B. Angles that are both acute and adjacent to each other
• C. Angles that are supplementary and form a straight line
• D. Angles that are vertical angles formed by intersecting lines

Answer: (A)

Verified step by step guidance

1. Understand the definition of coterminal angles: Coterminal angles are angles in standard position that share the same initial side and the same terminal side, but may differ by full rotations of 360 degrees.
2. Recall that an angle in standard position is drawn with its vertex at the origin and its initial side along the positive x-axis on the coordinate plane.
3. Recognize that adding or subtracting multiples of 360° to an angle results in another angle that ends at the same position on the coordinate plane, hence they are coterminal.
4. Apply this to the example given: 30° and 390° differ by 360° (390° - 30° = 360°), so they have the same terminal side and are coterminal.
5. Contrast this with other angle pairs: acute adjacent angles, supplementary angles forming a straight line, and vertical angles do not necessarily share the same terminal side and thus are not coterminal.