An illustration shows five rays with points near the arrows labeled A, B, C, D, and E in a counterclockwise direction, emerging from a common point labeled O. The points A, O, and E fall on a straight line. All the four angles are marked but unlabeled.

Question

Which angle(s) are adjacent to ∠DOC ?

(1 point)
Responses

∠AOD
angle upper A upper O upper D

∠EOD and ∠COB
angle upper E upper O upper D and angle upper C upper O upper B

∠DOB
angle upper D upper O upper B

∠AOB and ∠EOA

Answer 1

To determine which angles are adjacent to ∠DOC, we need to consider the layout of the rays and the angles formed at point O.

Angles are adjacent if they share a common side and vertex, without overlapping.

Given the options, let's evaluate each:

1. ∠AOD: This angle shares the side OD with ∠DOC and has the vertex O, so it is adjacent to ∠DOC.

2. ∠EOD and ∠COB:

   • ∠EOD shares the side OD and vertex O, so it is adjacent to ∠DOC.
   • ∠COB shares the side OC and vertex O, hence it is not adjacent to ∠DOC.

3. ∠DOB: This angle is adjacent because it shares side OD and vertex O with ∠DOC.

4. ∠AOB and ∠EOA:

   • ∠AOB shares the side OA with ∠DOC, making it adjacent.
   • ∠EOA shares the side OE, which is part of the same line as A and does not overlap with ∠DOC, confirming its status as adjacent to ∠DOC.

So the angles adjacent to ∠DOC are:

• ∠AOD
• ∠EOD
• ∠DOB
• ∠AOB
• ∠EOA

The correct meaningful responses based on the options available would be:

• ∠AOD
• ∠EOD and ∠COB (only ∠EOD is adjacent)
• ∠DOB
• ∠AOB and ∠EOA (both are adjacent)

In conclusion, the correct angles adjacent to ∠DOC are:

• ∠AOD
• ∠EOD
• ∠DOB
• ∠AOB
• ∠EOA

However, since we have to select from the available responses, the best candidate that fits the question (considering options listed) would be ∠EOD and ∠COB since it includes one adjacent angle. If selectivity is required, go with all instances that clearly show adjacent angles like ∠AOD and ∠DOB.