Given two intersecting lines in the coordinate plane, which diagram shows angles $1$ and $2$ as vertical angles in standard position?

• A. Diagram B: Angles $1$ and $2$ are adjacent and share a common side.
• B. Diagram D: Angles $1$ and $2$ are complementary and share a common side.
• C. Diagram C: Angles $1$ and $2$ are supplementary but not opposite each other.
• D. Diagram A: Angles $1$ and $2$ are formed by two intersecting lines, sharing only the vertex and lying opposite each other.

Answer: (D)

Verified step by step guidance

1. Recall the definition of vertical angles: Vertical angles are the pairs of opposite angles made by two intersecting lines. They share a common vertex but do not share a common side.
2. Identify the key characteristics of vertical angles: they are congruent (equal in measure) and are located across from each other at the intersection point of the two lines.
3. Analyze each diagram based on these characteristics: check if angles 1 and 2 share only a vertex and lie opposite each other without sharing a side.
4. Note that adjacent angles share a common side, so if angles 1 and 2 are adjacent, they cannot be vertical angles.
5. Conclude that the diagram where angles 1 and 2 are opposite each other at the intersection, sharing only the vertex, correctly shows vertical angles in standard position.