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 in each column to show a pair of angles that represents a counterexample. ∠fgh ∠fgm angle 2

Explanation:

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

When a transversal intersects parallel lines, adjacent angles are supplementary (linear - pair postulate), but non - adjacent angles can also be supplementary. For example, same - side interior angles are non - adjacent and supplementary.

Step2: Analyze the given angles

$\angle FGH$ and $\angle KMO$ are same - side interior angles. They are non - adjacent and supplementary. Also, $\angle FGM$ and $\angle PMO$ are same - side interior angles, non - adjacent and supplementary.

Answer:

For $\angle FGH$, a counter - example angle could be $\angle KMO$; for $\angle FGM$, a counter - example angle could be $\angle PMO$