Final answer:
Adjacent angles are defined as two angles that share a common vertex and side but do not overlap. They are crucial for understanding geometric shapes and vector relationships in mathematics.
Step-by-step explanation:
The correct definition for adjacent angles is: B) Two angles that share a common vertex and side but have no common interior points. This means that adjacent angles are next to each other on a flat surface and they share a common side, which also means they extend in different directions from the same point (the vertex) but do not overlap. It’s important to make these distinctions in geometry to understand the relationships between angles and how they interact within various shapes and figures. For example, in a triangle, which is a three-sided polygon, the sum of its interior angles is always 180°. This knowledge is useful in solving for unknown angles within the triangle.
In the world of vectors, two vectors that point in the same direction are called parallel vectors, and when they are perpendicular to each other, they are orthogonal vectors. These relationships are essential for understanding vector operations and properties such as vector addition and dot product, which can, in turn, inform us about the angles between two vectors in a space.