Adjacent angles are two angles in a plane that have a common vertex and a common side. They do not have any common interior points. In other words, they do not share any "inside space."
The 3 roads above form two adjacent angles. The two angles formed share a common side of Park Road and the intersection of the 3 roads is the common vertex for the 2 adjacent angles. In this case, it would probably be wise to put a traffic signal at the vertex.
Knowing that 2 angles are adjacent is useful for finding the measure of one of the adjacent angles given the measure of the other.
In the diagram above ∠POM = 67° and ∠MON=52°. Since ∠PON and ∠MON are adjacent angles the measure of their sum is ∠POM,
|∠PON + ∠MON = ∠POM|
|∠PON + 52° = 67°|
|∠PON = 15°|
Adjacent sides are two sides of a polygon or other shapes that have a common vertex.
In the triangle above, AB and BC are adjacent sides since they share the same vertex, B. AB and AC and AC and BC are also adjacent sides.
In the parallelogram above, sides RS and SV, RS and RW are two examples of adjacent sides since they have common vertices. In contrast, sides RS and WV and RW and SV are not adjacent sides since they do not share a vertex.