Mathematics

How many pairs of adjacent angles, in all, can you name in figure?


SOLUTION
Two angles are Adjacent when they have a common side and a common vertex (corner point) and don't overlap.
So, $$point\ O$$ is a common vertex for all angles.
When $$OD$$ is common side,
$$\angle EOD\ and\ \angle AOD,\  \angle EOD\ and\ \angle BOD,\  \angle EOD\ and\ \angle COD$$ are pair of adjacent angles.
Similarly, when $$OC$$ is common side,
$$\angle EOC\ and\ \angle AOC,\  \angle EOC\ and\ \angle BOC,\  \angle DOC\ and\ \angle AOC,\  \angle DOC\ and\ \angle BOC$$ are pair of adjacent angles.
When $$OB$$ is common side,
$$\angle AOB\ and\ \angle EOB,\  \angle AOB\ and\ \angle BOD,\  \angle AOB\ and\ \angle COB$$ are pair of adjacent angles.

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