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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

∠DOB
angle upper D upper O upper B

∠EOD
and ∠COB

1 answer

To determine which angles are adjacent to ∠DOC, we need to identify the angles formed by the rays and how they are positioned in relation to ∠DOC.

In the provided scenario:

  • The rays are labeled A, B, C, D, and E in a counterclockwise direction from point O.
  • A straight line is formed by points A, O, and E.

Adjacent angles share a common ray and do not overlap.

Given that:

  • ∠DOC is formed by rays OD and OC.
  • Angles adjacent to ∠DOC would be the angles that share ray OD or ray OC.

Analyzing the options:

  1. ∠AOD - Shares ray OD.
  2. ∠AOB and ∠EOA - Shares ray OA, not applicable.
  3. ∠DOB - Shares ray OD.
  4. ∠EOD and ∠COB - Shares ray OD and ray OC, respectively.

Therefore, the angles that are adjacent to ∠DOC are:

  • ∠AOD
  • ∠DOB
  • ∠EOD (which shares ray OD)

Hence, the correct responses indicating adjacency are:

  • ∠AOD
  • ∠DOB
  • ∠EOD

Based on your provided options, the best answer would be:

  • ∠AOD, ∠DOB, and ∠EOD.

However, since option 4 includes both ∠EOD and ∠COB, it is the most comprehensive response. Therefore,

The answer is: ∠EOD and ∠COB.