Given: ∠1 and ∠2 are supplementary.
prove: ℓ ∥ m

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 since ∠2 and ∠3 are corresponding angles, ℓ ∥ m.

∠2 and ∠3 are supplementary

∠2 ≅ ∠3

∠2 = ∠3

∠2 and ∠3 are not supplementary