Question

kori uses the diagram to analyze the given statement. \when a transversal intersects parallel lines, two angles are supplementary if and only if they are adjacent angles.\ select one angle from each column to show a pair of angles that represents a counterexample. angle 1 angle 2 ∠fgh ∠fgm

Explanation:

Step1: Recall angle - relationships in parallel lines cut by a transversal

When a transversal intersects parallel lines, there are several angle - relationships. Supplementary angles add up to 180 degrees, and adjacent angles share a common side and a common vertex.

Step2: Identify non - adjacent supplementary angles

In the given diagram of parallel lines \(FI\) and \(KP\) cut by transversal \(HO\), \(\angle FGH\) and \(\angle GNP\) are corresponding angles. Also, \(\angle FGH\) and \(\angle GNK\) are non - adjacent supplementary angles. Another pair of non - adjacent supplementary angles is \(\angle FGM\) and \(\angle GNP\). We can choose \(\angle FGH\) and \(\angle GNK\) (or other non - adjacent supplementary angle pairs). For the given options, if we consider the properties of angles formed by parallel lines and a transversal, we know that non - adjacent angles can be supplementary. For example, \(\angle FGH\) and \(\angle GNK\) are non - adjacent and supplementary.

Answer:

\(\angle FGH\), \(\angle GNK\) (Note: There are other valid non - adjacent supplementary angle pairs in the diagram that can also be chosen as a counter - example to the given false statement)