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

∠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

∠DOB

Answer 1

To determine which angle(s) are adjacent to ∠DOC, we first need to understand that adjacent angles share a common vertex and a common side.

1. Identify the angles formed by the rays:

   • ∠AOB (between rays AO and OB)
   • ∠DOC (between rays DO and OC)
   • ∠EOD (between rays EO and OD)
   • ∠COB (between rays CO and OB)
   • ∠AOD (between rays AO and OD)

2. Consider the relationships:

   • Angles adjacent to ∠DOC would be angles that share the vertex O and one of the rays (DO or OC).

3. Analyzing adjacent angles:

   • Adjacent to ∠DOC:
     • ∠AOD (shares ray OD with ∠DOC)
     • ∠COB (shares ray OC with ∠DOC)
     • ∠EOD (shares ray OD; it's not adjacent because it is not sharing ray OC)

From this, the angles adjacent to ∠DOC are identified as:

Correct response:

• ∠AOD and ∠COB.