Which of the following statements is true about angles in standard position?

• A. The terminal side of an angle in standard position always lies along the positive $y$-axis.
• B. Angles in standard position are always acute angles.
• C. The initial side of an angle in standard position always lies along the positive $x$-axis.
• D. The vertex of an angle in standard position is always at the origin.

Answer: (D)

Verified step by step guidance

1. Recall the definition of an angle in standard position: it has its vertex at the origin of the coordinate plane.
2. Understand that the initial side of the angle in standard position always lies along the positive x-axis.
3. Recognize that the terminal side of the angle can lie anywhere in the coordinate plane, not necessarily along the positive y-axis.
4. Note that angles in standard position can be acute, right, obtuse, or even reflex; they are not restricted to being acute.
5. Conclude that the true statements are: the vertex is at the origin, and the initial side lies along the positive x-axis.