Would my answer be correct?

Question

Lines m and n are cut by a transversal, as shown in the figure.

Given line m is not parallel to line n, prove ∠4 is not congruent to ∠6 by contradiction. (2 points for the assumption statement, 4 points for the remainder of the proof)

By contradiction, <4 is not congruent to <6, hence let's say ∠4 ≠∠6. Because those angles match, line m // line n. The original assumption cannot be valid because this goes against the information provided, which states that line m is not parallel to line n.

m not parallel, to n. Can prove angle 4 = angle 6.

angle 6 ≠angle 2 because only parallel construction

of m and n would create equal angles. Angle 4= angle 2

because opposite vertex angles equal each other.

therefore, angle 6≠angle 4,, contradiction.

Would this be correct and if not, whats the answer

Answer 1

Assume that ∠4 ≅ ∠6

∠2 ≅ ∠4 and ∠8 ≅ ∠6 (vertical angles)

∠2 ≅ ∠8

m ll n (alternate interior angles)

**CONTRADICTION**

Therefore, ∠4 and ∠6 are not congruent