1. The problem asks to identify which two angles are adjacent in a four-ray angle diagram with angles labeled 1, 2, 3, and 4 around a common vertex. 2. Adjacent angles share a common side and a common vertex but do not overlap. 3. In the diagram, angles 2 and 3 share a common ray and vertex, so they are adjacent. 4. Angles 1 and 3 do not share a common side, so they are not adjacent. 5. Angles 2 and 4 are opposite each other and do not share a side, so they are not adjacent. Final answer: The two adjacent angles are 2 and 3.