a linear pair
A linear pair is the special case of two adjacent angles whose outer sides form a straight line. Stand a flagpole on the ground and lean it over: on one side of the pole the angle to the ground is some amount, and on the other side it is the rest of the flat 180. Those two angles, leaning against each other along the same straight ground, are a linear pair.
Precisely: angles ABC and CBD form a linear pair when ray BC is shared, and rays BA and BD point in exactly opposite directions, so that A, B, D are collinear. Because A-B-D is a straight angle measuring 180, the two pieces must satisfy m(angle ABC) + m(angle CBD) = 180. This is the linear-pair postulate (or theorem): the angles in a linear pair are supplementary. So if one is 110, the other is 70 — they always trade off to fill the half-turn.
Linear pairs are the engine behind the vertical-angles proof and behind much of early angle chasing: every time a ray stands on a line, it cuts a linear pair, instantly giving you two angles that add to 180. Note the difference from merely supplementary angles: any two angles summing to 180 are supplementary, but a linear pair must also be adjacent and sit on one straight line.
Ray BC stands on line AD at point B. The angle on the left, angle ABC, measures 130 degrees. Because ABC and CBD form a linear pair, angle CBD = 180 - 130 = 50 degrees.
A ray on a line makes a linear pair, and the two angles add to 180.
Every linear pair is supplementary, but not every supplementary pair is a linear pair: supplementary only requires the measures to add to 180, while a linear pair must be adjacent and lie along one straight line.