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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

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

∠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
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1 answer

To determine which angle(s) are adjacent to ∠DOC, we should consider the definition of adjacent angles. Adjacent angles share a common vertex and a common side but do not overlap.

From the arrangement of the rays emerging from point O:

  • ∠DOC is formed by rays OD and OC.
  • Adjacent to ∠DOC would be angles that share one side with ∠DOC (either ray OD or ray OC) and do not overlap with ∠DOC.

Looking at the options provided:

  • ∠AOD: Shares ray OD with ∠DOC, so it is adjacent.
  • ∠EOD: Shares ray OD with ∠DOC, so it is adjacent.
  • ∠COB: Shares ray OC with ∠DOC, so it is adjacent.
  • ∠AOB: Shares ray OA (not adjacent).
  • ∠EOA: Shares ray OA (not adjacent).
  • ∠DOB: Shares ray OD with ∠DOC (adjacent).

Thus, the angles adjacent to ∠DOC are:

  • ∠AOD
  • ∠EOD
  • ∠COB
  • ∠DOB

Based on the original options provided, the most comprehensive correct response would be option 2: ∠EOD and ∠COB.

This includes angles that share a side with ∠DOC.