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 counter - example.
angle 1 angle 2
∠fgm ∠kmg

Explanation:

Step1: Recall properties of parallel - lines and transversals

When a transversal intersects parallel lines, there are several angle - relationships. Supplementary angles add up to 180 degrees. Adjacent angles share a common side and a common vertex. We need to find non - adjacent angles that are supplementary.

Step2: Identify corresponding and same - side interior angles

Corresponding angles are equal when lines are parallel. Same - side interior angles are supplementary. For example, $\angle FGM$ and $\angle KMG$ are same - side interior angles. They are not adjacent (they do not share a common side and a common vertex in the adjacent - angle sense) but they are supplementary because when a transversal intersects parallel lines $FI$ and $KP$, same - side interior angles sum to 180 degrees.

Answer:

Angle 1: $\angle FGM$, Angle 2: $\angle KMG$