Final answer:
Adjacent angles are two angles that share a vertex and side but do not overlap. They are significant in geometrical shapes and in vector analysis where they can represent various angle relationships such as 90° or 180° formed by orthogonal vectors or sides of polygons.
Step-by-step explanation:
Adjacent angles are two angles that have a common vertex and a common side but do not overlap. In geometry, adjacent angles often share a bordering line and, in the case of polygons, form an interior angle relationship. For instance, in a trigonal bipyramidal molecular geometry, the angles can be of 90° or 120°, which are types of adjacent angles when referring to the equatorial and axial positions related to the central atom.
Moreover, understanding adjacent angles is crucial in the context of vector analysis in physics, where vectors in a plane can be orthogonal (perpendicular) or parallel, thus forming adjacent angles of 90 degrees and 0 degrees, respectively. In trigonometry, it is also important when looking at the components of a vector in a Cartesian plane or when analyzing the angles within a right triangle. In essence, recognizing adjacent angles aids in solving various geometric and trigonometric problems.