A angle it is the part of the plane comprised between two rays that have a common origin. The rays are called sides and the common origin is vertex.
Two angles are adjacent if they have a side, the vertex in common and are supplementary.
The adjacent angles they are those that have one side and a vertex in common, in addition to that their other two sides are opposite rays. Two adjacent angles are both consecutive and supplementary, because together they are equal to a straight angle (180⁰).
The angle α is adjacent to β because: 1) they have one side in common (the line CB), 2) the vertex in common (point B) and 3) both are consecutive and add up to 180⁰, that is, they are supplementary.
A and B they are not adjacent. They share the vertex and one side, but they are not supplementary. This is a typical error, sometimes the slip is made to name adjacent consecutive angles.
Usually, two angles are adjacent if:
- They have a common side.
- They have the vertex in common.
- They are consecutive.
- They are supplementary (their sum results in 180⁰).
- The breasts of the adjacent angles are the same, example:
- sin α = sin (180⁰ - α)
- sin α = sin (π - α)
- sin 120⁰ = sin 60⁰
- The cosines of the adjacent angles are of equal absolute value, but of inverse sign, example:
- cos α = - cos (180⁰ - α)
- cos α = - cos (π - α)
- cos 120⁰ = - cos 60⁰