Which of the following best describes an angle in standard position in the coordinate plane?

• A. Its vertex is at the origin and its initial side lies along the positive $x$-axis.
• B. Its vertex is at any point in the plane and its initial side can be in any direction.
• C. Its vertex is at the origin and its terminal side lies along the positive $x$-axis.
• D. Its vertex is at the origin and its initial side lies along the negative $y$-axis.

Answer: (A)

Verified step by step guidance

1. Recall the definition of an angle in standard position: it is an angle placed in the coordinate plane such that its vertex is at the origin (0,0).
2. Understand that the initial side of the angle is fixed along the positive x-axis, which serves as the reference line from which the angle is measured.
3. The terminal side of the angle can rotate from the initial side, either counterclockwise for positive angles or clockwise for negative angles.
4. Review the options given and identify which one matches the definition: the vertex must be at the origin, and the initial side must lie along the positive x-axis.
5. Conclude that the correct description is the one stating: 'Its vertex is at the origin and its initial side lies along the positive x-axis.'