In the context of angles in standard position, which of the following pairs of angles are considered vertical angles?

• A. Angles whose terminal sides coincide after a full rotation
• B. Angles that have the same measure but different initial sides
• C. Angles that share the same initial side but have different terminal sides
• D. Angles whose sides form two pairs of opposite rays and intersect at a common vertex

Answer: (D)

Verified step by step guidance

1. Recall the definition of vertical angles: Vertical angles are pairs of angles formed when two lines intersect, and their sides form two pairs of opposite rays.
2. Understand that opposite rays are two rays that share a common endpoint and extend in exactly opposite directions, forming a straight line.
3. Identify that vertical angles share a common vertex (the point of intersection) and their sides are formed by these opposite rays, making the angles opposite each other.
4. Compare the given options to this definition: angles whose sides form two pairs of opposite rays and intersect at a common vertex fit the criteria for vertical angles.
5. Conclude that the correct pair of vertical angles are those whose sides form two pairs of opposite rays and intersect at a common vertex, as this matches the formal geometric definition.