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 properties of parallel - lines and transversals

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

Step2: Analyze the statement

The statement claims that two angles are supplementary if and only if they are adjacent. We need to find non - adjacent supplementary angles.

Step3: Identify non - adjacent supplementary angles

In the given diagram of parallel lines \(FI\) and \(KP\) intersected by transversal \(HO\), \(\angle FGH\) and \(\angle GMP\) are corresponding angles. Also, \(\angle FGM\) and \(\angle GMP\) are same - side interior angles. Same - side interior angles are supplementary. \(\angle FGM\) and \(\angle GMP\) are non - adjacent and supplementary. So, we can choose \(\angle FGM\) from the first column and \(\angle GMP\) from the second column as a counter - example.

Answer:

\(\angle FGM\), \(\angle GMP\)