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Adjacent Angles Definition. Adjacent angles are two angles that share a common side and a common vertex, and do not overlap. In the given diagram, the angles $\angle ABD$ and $\angle CBD$ are adjacent angles. They share the common arm or common side BD and a common vertex B.
Adjacent angles are the angles that have a common arm (side) and a common vertex, however, they do not overlap. An angle is formed when two rays meet at a common endpoint and adjacent angles are those angles that are always placed next to each other.
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Since an angle is formed when two rays meet at a common endpoint, adjacent angles are simply two angles that are directly next to each other. Adjacent angles can be complementary angles or supplementary angles. For example, in this diagram, angle XW Y X WY is adjacent to angle Y W Z YW Z.
It is best to learn to understand whether the angles are adjacent or not on specific examples. EXAMPLE: In each case determine whether the angles 1 and 2 are adjacent or not. SOLUTION: a) Pair of angles ∠1 and ∠2 share the common vertex O and common arm $\vec {OB}$, so these angles are adjacent.
Any two angles that share a common ray or side, a common vertex, and whose interiors do not overlap are called adjacent angles. For example, look at the image below, the interiors of ∠ABD and ∠CBD don’t overlap, and hence they are adjacent angles.
Illustrated definition of Adjacent Angles: Two angles that have a common side and a common vertex (corner point), and dont overlap.
