To determine which angle(s) are adjacent to ∠DOC, we should consider the definition of adjacent angles. Adjacent angles share a common vertex and a common side but do not overlap.
From the arrangement of the rays emerging from point O:
- ∠DOC is formed by rays OD and OC.
- Adjacent to ∠DOC would be angles that share one side with ∠DOC (either ray OD or ray OC) and do not overlap with ∠DOC.
Looking at the options provided:
- ∠AOD: Shares ray OD with ∠DOC, so it is adjacent.
- ∠EOD: Shares ray OD with ∠DOC, so it is adjacent.
- ∠COB: Shares ray OC with ∠DOC, so it is adjacent.
- ∠AOB: Shares ray OA (not adjacent).
- ∠EOA: Shares ray OA (not adjacent).
- ∠DOB: Shares ray OD with ∠DOC (adjacent).
Thus, the angles adjacent to ∠DOC are:
- ∠AOD
- ∠EOD
- ∠COB
- ∠DOB
Based on the original options provided, the most comprehensive correct response would be option 2: ∠EOD and ∠COB.
This includes angles that share a side with ∠DOC.