To determine if two angles are adjacent, they must meet two criteria:
- They must share a common vertex.
- They must share a common ray (side).
Based on your options, if the two angles satisfy both conditions, the response would be: "Yes, they share a common vertex." and "Yes, they share a common ray."
If either condition is not met, then they are not adjacent, and the appropriate response would be either "No, they do not share a common vertex." or "No, they do not share a common ray."
If you provide additional context or a visual representation of the angles, I would be able to give a more specific answer.