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Adjacent Angles Quick Check

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Question
Use the image to answer the 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

∠EOD
and ∠COB
angle upper E upper O upper D and angle upper C 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
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1 answer

In the scenario described, to determine which angles are adjacent to ∠DOC, we need to identify the angles that share a common side and vertex with ∠DOC without overlapping.

From the description:

  • ∠DOB (angle upper D upper O upper B) shares the side OD and the vertex O with ∠DOC.
  • ∠EOD (angle upper E upper O upper D) shares the side OD and the vertex O with ∠DOC.
  • ∠COB (angle upper C upper O upper B) shares the side OC and the vertex O with ∠DOC.
  • ∠AOD (angle upper A upper O upper D) shares the side OA and the vertex O but is not adjacent since it does not share a ray with ∠DOC.
  • ∠AOB (angle upper A upper O upper B) shares the vertex O, but does not share a ray with ∠DOC.
  • ∠EOA (angle upper E upper O upper A) shares the vertex O, but does not share a ray with ∠DOC.

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

  • ∠DOB (∠D O B)
  • ∠EOD (∠E O D)
  • ∠COB (∠C O B)

The best response that includes adjacent angles to ∠DOC is:

∠DOB and ∠EOD and ∠COB.

If you need to select exactly two angles, then either ∠DOB or ∠EOD would be sufficient, but the combination of the three listed ensures clear identification of adjacent angles.