Which of the following pairs of angles are adjacent angles in standard position?

• A. Two angles that have the same initial side and their terminal sides are on opposite sides of the initial side
• B. Two angles that have the same initial side and their terminal sides are the same
• C. Two angles that have different initial sides but the same terminal side
• D. Two angles that have the same initial side and their terminal sides are not the same but do not overlap except at the initial side

Answer: (D)

Verified step by step guidance

1. Recall the definition of adjacent angles in standard position: they share the same initial side, and their terminal sides are next to each other without overlapping, meeting only at the initial side.
2. Analyze each option by checking if the angles have the same initial side, which is a requirement for adjacency in standard position.
3. For the first option, note that the terminal sides are on opposite sides of the initial side, meaning they do not lie next to each other, so they are not adjacent.
4. For the second option, the terminal sides are the same, so the angles overlap completely, which means they are not adjacent but coincident.
5. For the third option, the angles have different initial sides, so they cannot be adjacent in standard position regardless of their terminal sides.