Use the image to answer the question.

Question

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.

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.

Which angle(s) are adjacent to ∠DOC
?

(1 point)
Responses

∠DOB
angle upper D upper O upper B

∠AOD
angle upper A upper O upper D

∠AOB
and ∠EOA
angle upper A upper O upper B and angle upper E upper O upper A

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

Answer 1

To determine which angles are adjacent to ∠DOC, we need to consider the positioning of points A, B, C, D, and E in relation to point O.

In a setup where we have the common point O with rays leading to A, B, C, D, and E in a counterclockwise direction, ∠DOC is formed between rays OD and OC.

Adjacent angles to ∠DOC would be the angles formed by the rays that share a side with OD or OC. Therefore:

1. ∠DOB (angle formed by rays OD and OB) is adjacent to ∠DOC.
2. ∠EOA (the angle formed by rays EO and OA) is adjacent as it shares ray OA with ∠DOC.

Thereby, both ∠DOB and ∠EOA qualify as being adjacent to ∠DOC.

Based on the possible responses, the correct answer is:

∠AOB and ∠EOA (as they are adjacent without specifying the angles).

However, for more specific identification of angles adjacent to ∠DOC:

• This would be especially applicable for ∠EOD and ∠COB as they both share either one of the rays.

Thus the final correct response to the question is:

∠EOD and ∠COB (these are specifically adjacent to ∠DOC).