A linear pair is a pair of adjacent angles formed when two lines intersect each other at a single point. The two angles of a linear pair are always adjacent angles, which means they share a common vertex and a common arm but do not overlap. They are also always supplementary, which means their measures add up to 180 degrees. In other words, they together form a straight angle. Some key properties of linear pairs of angles include:
- The angles in a linear pair are supplementary (add up to 180 degrees) .
- A linear pair of angles are always adjacent angles.
- A linear pair of angles always form a straight line.
- Two angles forming a linear pair have a common vertex and a common arm. Their non-common sides are opposite rays that form a line.
The linear pair postulate states that if two angles form a linear pair, they are supplementary. However, the converse of this postulate is not true. It means that if two angles are supplementary, they do not necessarily form a linear pair of angles.
