Supplementary angles and linear pairs are two concepts in geometry that deal with angles, but they have distinct definitions and situations.
Supplementary angles are defined as two angles whose measures add up to 180 degrees. For example, if one angle measures 110 degrees, the other angle must measure 70 degrees to be supplementary: 110° + 70° = 180°.
On the other hand, a linear pair consists of two adjacent angles formed when two lines intersect. The key characteristic of a linear pair is that they always create supplementary angles because the angles share a common vertex and a common side, and they lie on a straight line. For instance, if two lines intersect to form one angle measuring 45 degrees, the adjacent angle, thus forming a linear pair, will measure 135 degrees: 45° + 135° = 180°.
In summary, while all linear pairs are supplementary, not all supplementary angles are linear pairs. The distinction lies in the angles’ arrangement: linear pairs must be adjacent angles formed by the intersection of two lines, while supplementary angles can exist independently of each other.