Question

use the diagram and the given information to determine if m || n, p || q, or neither.
given: ∠2 ≅ ∠11
m || n
p || q
neither

Explanation:

Step1: Recall parallel - line postulates

When two lines are cut by a transversal, certain angle - relationships indicate parallel lines. For example, corresponding angles, alternate interior angles, etc.

Step2: Analyze the given angles

\(\angle2\) and \(\angle11\) are not corresponding angles, alternate interior angles, or alternate exterior angles for either \(m\) and \(n\) or \(p\) and \(q\).

Step3: Make a conclusion

Since \(\angle2\cong\angle11\) does not satisfy the angle - relationships for parallel lines \(m\parallel n\) or \(p\parallel q\), the answer is neither.

Answer:

neither