The correct response is:
Yes, the two indicated angles share a common vertex.
Adjacent angles are defined as two angles that share a common vertex and a common side (ray). If the two indicated angles share a common vertex, then they are adjacent, even if they do not share a common ray. However, based on the phrasing of the given options, if they share a common ray, that would also imply adjacency. If you know that they share a common vertex, then it confirms they are adjacent.
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