To solve the problem, we need to utilize the given information that [tex]\(\angle 1\)[/tex] and [tex]\(\angle 2\)[/tex] form a linear pair and then apply the definition of a linear pair to derive a new statement.
Let's break it down step-by-step:
1. Given Information:
- Statement: [tex]\(\angle 1\)[/tex] and [tex]\(\angle 2\)[/tex] form a linear pair.
- Reason: Given.
2. Apply the Definition of Linear Pair:
- When two angles form a linear pair, their measures sum up to 180 degrees because they form a straight angle. This is the definition of a linear pair.
Based on this definition, we can derive the following statement:
- Statement: [tex]\(\angle 1\)[/tex] and [tex]\(\angle 2\)[/tex] are supplementary.
- Reason: If two angles are a linear pair, then they form a straight angle (definition of a linear pair).
So, filling in the given information and the reasoning into the table:
[tex]\[
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|}{ Statements } & \multicolumn{1}{c|}{ Reasons } \\
\hline 1. $\angle 1$ and $\angle 2$ form a linear pair. & 1. Given \\
\hline
2. $\angle 1$ and $\angle 2$ are supplementary. & \begin{tabular}{l} 2. If two angles are a linear pair, then they form \\ a straight angle. (definition of linear pair)\end{tabular} \\
\hline
\end{tabular}
\][/tex]
Thus, the statement that can be made using the given information and the definition of linear pair is:
- [tex]\(\angle 1\)[/tex] and [tex]\(\angle 2\)[/tex] are supplementary.
