Assumption: Let's assume that ∠4 is congruent to ∠6.
Proof by contradiction:
1. If ∠4 is congruent to ∠6, it implies that corresponding angles formed by line m and line n are congruent due to the transversal property.
2. Let's consider ∠1 and ∠5, which are corresponding angles formed by line m and line n.
3. If ∠4 is congruent to ∠6, it would mean that ∠1 is congruent to ∠5 as well.
4. However, this contradicts the given statement that line m is not parallel to line n. When a transversal intersects two lines, the corresponding angles are congruent only if the lines are parallel.
5. Since line m is not parallel to line n, ∠1 cannot be congruent to ∠5.
6. Therefore, our assumption that ∠4 is congruent to ∠6 leads to a contradiction.
By the contradiction, we can conclude that ∠4 is not congruent to ∠6.
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