Q:

What are two adjacent angles whose non-common sides are opposite rays?

A:

Two adjacent angles whose non-common sides are opposite rays form a linear pair. The two angles combine to be 180 degrees, and the two opposite rays create a straight line. The adjacent angles appear from a single ray that starts at the midpoint of the opposite rays.

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The adjacent angles are supplementary in that they add up to 180 degrees. For instance, one angle can be 45 degrees and the other 135 degrees. If two congruent angles create a linear pair, they are right angles at 90 degrees each. Not all supplementary angles are linear pairs, but all linear pairs are supplementary angles. The two rays combine to form a straight line with one point that originates the ray for the linear pair.

There can be many linear pairs that originate from the same point along the two opposite rays. A ray is a line with a firm origination point that goes infinitely in one direction. The opposite rays start at one end point and go infinitely in opposite directions.

Linear pairs have real-world applications in chemistry as it relates to the structure of chemicals and molecules. Knowing the three-dimensional arrangement of atoms and molecules gives scientists clues as to a substance's reactivity, color, magnetism and biological activity.

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