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$\angle 1 $ and $\angle 2$ are adjacent . So are $\angle AOD$ and $\angle BOD$ also adjacent. ? I am confused.

EDIT:

Suppose the point $C$ is not in the diagram , then in this case are $\angle AOD$ and $\angle BOD$ adjacent ?.

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2 Answers

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Definition. Two coplanar angles are said to be adjacent if they share a common vertex and a common side but no common interior points.

While $\angle AOD$ and $\angle BOD$ share a common vertex (point $0$) and a common side ($\overrightarrow{OD}$), they are not adjacent since $C$ is a common interior point of the two angles.

Examples of adjacent angles in the diagram include $\angle AOB$ and $\angle BOC$, $\angle AOB$ and $\angle BOD$, $\angle AOC$ and $\angle COD$, and $\angle BOC$ and $\angle COD$.

Edit: In your new diagram, $\angle AOD$ and $\angle BOD$ are not adjacent since they share interior points. For instance, if $\overrightarrow{OC}$ is the angle bisector of $\angle BOD$, then point $C$ is in the interior of both $\angle AOD$ and $\angle BOD$.

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No, they are not. They share the "space" occupied by angle $\angle AOC$. $2$ angles are adjacent if they share a side, and have a common vertex. Angles $\angle AOB$, and $\angle COB$ are adjacent.

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