Final answer:
The Linear Pair Theorem concerns adjacent angles forming a line and is essential in geometry, indicating that their measures sum to 180 degrees. It applies the commutative property and relates to data pairs in linear equations.
Step-by-step explanation:
The Linear Pair Theorem or the Supplement Theorem is a principle in geometry that deals with adjacent angles that form a straight line. If two angles form a linear pair, they are supplementary, which means their angle measures add up to 180 degrees. This theorem is fundamental in understanding various mathematical relationships and proving other geometric propositions.
For instance, if angle 1 and angle 2 form a linear pair, i.e., they are adjacent and their non-common sides form a straight line, then:
angle 1 + angle 2 = 180 degrees
This concept adheres to the commutative property of addition, where the order of addition does not affect the outcome, similar to how A + B = B + A, which applies to ordinary numbers as well. When substituting any two data pairs into an equation derived from a linear relationship, one might use values from experimental data or a given data table, ensuring that the substitutions reflect the correct corresponding variables.