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 $DOC$.