Question

what is the missing piece of information in the paragraph proof? proof: it is given that ∠1 and ∠2 are supplementary. ∠1 and ∠3 are also supplementary, so ∠2 ≅ ∠3. since ____ are corresponding angles, l ∥ m. ∠2 and ∠1 ∠1 and ∠3 ∠2 and ∠3 ∠1 and ∠2

Explanation:

Corresponding - angles postulate states that if two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. Here, we need congruent corresponding angles to prove \(l\parallel m\). Among the given angle - pairs, \(\angle2\) and \(\angle3\) are not corresponding angles, \(\angle1\) and \(\angle2\) are not corresponding angles, \(\angle1\) and \(\angle3\) are not corresponding angles. The pair of corresponding angles that would help in the proof of \(l\parallel m\) is \(\angle2\) and \(\angle3\) as we have already shown \(\angle2\cong\angle3\).

Answer:

\(\angle2\) and \(\angle3\)