Ineed with this question. i'm giving all the points i have.

∠4 ≅ ∠5

Explanation:

In order to prove that lines are parallel, one of the congruent angles must be from one of the parallel lines and the other congruent angle must be from the other parallel line.

angles 1, 2, 3, and 4 are on line l

angles 5,6,7, and 8 are on line m

so, you must have one angle from line l and the other from line m

Option 1 is ∠2 ≅ ∠3 which are both on line l so this won't work

Option 2 is ∠7 + ∠8 = 180 which are both on line m so this won't work

Option 3 is ∠4 ≅ ∠5, one is on line l and the other on line m so THIS WORKS by the Converse of Alternate Interior Angles Theorem

Option 4 is ∠6 + ∠2 = 180, one is on line l and the other on line m but they are supplementary so this won't work. They need to be congruent in order to prove parallel lines by the Converse of Corresponding Angles Theorem.

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step-by-step explanation:

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