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.

How many angles are adjacent to angle DOC ?

Answer 1

To determine how many angles are adjacent to angle \( DOC \) in the illustration described, we first need to understand the concept of adjacent angles. Adjacent angles share a common vertex and a common side but do not overlap.

From the arrangement of the rays and the points:

1. Points \( D \) and \( C \) form angle \( DOC \).
2. The angles adjacent to angle \( DOC \) would be the angles that share the vertex \( O \) and one side along ray \( OD \) or ray \( OC \).

Given the counterclockwise arrangement of points A, B, C, D, and E:

• The rays are arranged such that:
  • Angle \( AOD \) is adjacent to angle \( DOC \).
  • Angle \( BOC \) is adjacent to angle \( DOC \).

Therefore, angle \( DOC \) has two adjacent angles:

• Angle \( AOD \)
• Angle \( BOC \)

In total, there are two angles adjacent to angle \( DOC \).