Understanding Adjacent Angles and their Relationships: Complementary and Supplementary Angles

adjacent angles

Adjacent angles are a pair of angles that have a common vertex and a common side, but do not overlap

Adjacent angles are a pair of angles that have a common vertex and a common side, but do not overlap. The two angles are side by side and share the same vertex and one side, while their other sides are not shared.

In the diagram below, ∠ABC and ∠CBD are adjacent angles:

A
/ \
/ \
/____\
B C D

In this case, angle ∠ABC and ∠CBD both share the common vertex B and the common side BC. However, they do not overlap, as their other sides (AB and CD) are not shared.

Adjacent angles can have various relationships based on the measures of the angles:

1. Adjacent angles can be complementary: If the sum of two adjacent angles is equal to 90 degrees, they are called complementary angles. In this case, one angle is the complement of the other.

2. Adjacent angles can be supplementary: If the sum of two adjacent angles is equal to 180 degrees, they are called supplementary angles. In this case, one angle is the supplement of the other.

Note that adjacent angles do not need to be complementary or supplementary. They can have any measure as long as they share a common vertex and side, but do not overlap.

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