Question

geometry (e) parallel lines quick quiz in the diagram to the right, a || b. 1.) list one pair of alternate exterior angles. 2.) what name do we give the angle - pair of ∠1 and ∠5? 3.) if m∠3 = 79.2°, what is m∠8? 4.) are ∠1 and ∠7 congruent or supplementary? briefly explain.

Explanation:

Step1: Identify alternate - exterior angles

For parallel lines \(a\parallel b\) cut by a transversal \(m\), \(\angle1\) and \(\angle8\) are alternate - exterior angles.

Step2: Recall angle - pair relationship for \(\angle1\) and \(\angle5\)

\(\angle1\) and \(\angle5\) are corresponding angles.

Step3: Use angle - congruence properties for parallel lines

Since \(a\parallel b\), \(\angle3\) and \(\angle8\) are vertical angles, so they are congruent. Given \(m\angle3 = 79.2^{\circ}\), then \(m\angle8=79.2^{\circ}\).

Step4: Analyze \(\angle1\) and \(\angle7\) relationship

\(\angle1\) and \(\angle7\) are corresponding angles. Since \(a\parallel b\), corresponding angles are congruent.

Answer:

1. One pair of alternate - exterior angles is \(\angle1\) and \(\angle8\).
2. The angle - pair of \(\angle1\) and \(\angle5\) is corresponding angles.
3. \(m\angle8 = 79.2^{\circ}\)
4. \(\angle1\) and \(\angle7\) are congruent because they are corresponding angles for parallel lines \(a\) and \(b\) cut by transversal \(m\).