what are adjacent angles?

Adjacent angles are two angles that share a common arm (side) and a common vertex, yet do not overlap. In other words, they are angles that are side by side, with the common side forming a line segment between the two angles.

Key characteristics of adjacent angles:

1. Common Arm (Side): Adjacent angles have a common side or arm, which is a line segment between the two angles.
2. Common Vertex: The angles share a common vertex, which is the point where the sides of the angles meet.
3. Do Not Overlap: Adjacent angles do not overlap or share any interior points. They are distinct angles that lie next to each other.
4. Form a Linear Pair: When the common side forms a straight line with the arms of the two angles, the adjacent angles are referred to as a linear pair. The sum of the measures of adjacent angles forming a linear pair is always 180 degrees.
5. Naming: Adjacent angles are often named with reference to the common side and the direction in which the angles are measured. For example, if ∠ABC and ∠CBD are adjacent angles, the common side is BC, and ∠ABC and ∠CBD are adjacent at vertex B.

In symbolic notation, if ∠ABC and ∠CBD are adjacent angles, it can be represented as:

∠ABC+∠CBD=measure of the linear pair=180∘∠ABC+∠CBD=measure of the linear pair=180∘

Understanding adjacent angles is essential in geometry, especially when working with angles formed by intersecting lines, parallel lines, or other geometric figures. The concept of adjacent angles is fundamental to various geometric principles and theorems.