In which diagram are angles $1$ and $2$ vertical angles?

• A. A diagram where two straight lines intersect and angles $1$ and $2$ are opposite each other at the intersection point
• B. A diagram where two lines meet at a point and angles $1$ and $2$ are adjacent and form a linear pair
• C. A diagram where two parallel lines are cut by a transversal and angles $1$ and $2$ are on the same side of the transversal
• D. A diagram where angles $1$ and $2$ are in different triangles that share a common vertex

Answer: (A)

Verified step by step guidance

1. Recall the definition of vertical angles: Vertical angles are the pairs of opposite angles made by two intersecting straight lines. They are always equal in measure.
2. Identify the key characteristic of vertical angles: they are formed when two straight lines intersect, and the angles are opposite each other at the point of intersection.
3. Analyze each option by checking if the angles labeled 1 and 2 are opposite angles formed by the intersection of two straight lines.
4. Eliminate options where angles 1 and 2 are adjacent (next to each other) or lie on the same side of a transversal, as these do not satisfy the condition for vertical angles.
5. Conclude that the correct diagram is the one where two straight lines intersect and angles 1 and 2 are opposite each other at the intersection point, because this matches the definition of vertical angles.