Question

1. lines f and g are parallel. which statement can you not deduce from this information?

∠1 = ∠8

∠4 = ∠7

m∠2 + m∠5 = 180

m∠3 + m∠8 = 180

Explanation:

Step1: Analyze \(\angle1=\angle8\)

Since \(\angle1 = \angle4\) (vertical angles) and \(\angle4=\angle8\) (corresponding angles as \(f\parallel g\)), by transitive property \(\angle1=\angle8\).

Step2: Analyze \(\angle4=\angle7\)

\(\angle4\) and \(\angle7\) are alternate - interior angles. For parallel lines \(f\) and \(g\) cut by a transversal, alternate - interior angles are equal. So \(\angle4=\angle7\).

Step3: Analyze \(m\angle2 + m\angle5=180\)

\(\angle2\) and \(\angle5\) are same - side interior angles. For parallel lines \(f\) and \(g\) cut by a transversal, same - side interior angles are supplementary. So \(m\angle2 + m\angle5 = 180\).

Step4: Analyze \(m\angle3 + m\angle8=180\)

\(\angle3=\angle2\) (vertical angles). There is no direct relationship (such as same - side interior, corresponding, or alternate - interior) between \(\angle2\) (or \(\angle3\)) and \(\angle8\) based on the parallel - line properties (corresponding angles, alternate - interior angles, same - side interior angles) to conclude that \(m\angle3 + m\angle8=180\).

Answer:

\(m\angle3 + m\angle8 = 180\)