Question

complete the statements below. we see that ∠1 and ∠2 are vertical angles. thus, ∠1 and ∠2 are congruent. so, m∠2 = 55°. we see that ∠2 and ∠3 are corresponding angles. and since the lines p and q are parallel, ∠2 and ∠3 are congruent. so, m∠3 = °. therefore, ∠1 and ∠3 are (choose one) we also see that ∠1 and ∠3 are (choose one) the relationship between ∠1 and ∠3 is an example of the following rule. when parallel lines are cut by a transversal, (choose one)

Explanation:

Step1: Recall angle - congruence properties

Given \(m\angle2 = 55^{\circ}\), and \(\angle2\) and \(\angle3\) are corresponding angles with parallel lines \(p\) and \(q\).

Step2: Use the property of corresponding angles

Since corresponding angles formed by parallel lines are congruent, \(m\angle3=m\angle2\).

Answer:

\(m\angle3 = 55^{\circ}\)
Since \(\angle1\) and \(\angle2\) are vertical - angles (congruent) and \(\angle2\) and \(\angle3\) are corresponding angles (congruent) with parallel lines \(p\) and \(q\):

• \(\angle1\) and \(\angle3\) are congruent.
• \(\angle1\) and \(\angle3\) are also alternate exterior angles (assuming the appropriate orientation of the transversal).
• When parallel lines are cut by a transversal, vertical - angles and corresponding angles are congruent, and alternate exterior angles are congruent. So the relationship between \(\angle1\) and \(\angle3\) is an example of the rule that when parallel lines are cut by a transversal, alternate exterior angles are congruent.