1. **State the problem:** We are given two parallel lines $m$ and $n$ cut by a transversal $t$. Angle 7 measures $75^\circ$. We need to find which angle among 3, 5, 2, and 6 is NOT congruent to angle 7. 2. **Recall angle relationships with parallel lines and a transversal:** - Corresponding angles are congruent. - Alternate interior angles are congruent. - Alternate exterior angles are congruent. - Consecutive interior angles are supplementary. 3. **Identify angle 7's position:** Angle 7 is at the bottom-left of the intersection of line $n$ and transversal $t$. 4. **Check each angle:** - Angle 3 is bottom-left at line $m$ and $t$ intersection (top). Angle 7 and angle 3 are alternate interior angles, so they are congruent: $\angle 3 = 75^\circ$. - Angle 5 is top-left at line $n$ and $t$ intersection (bottom). Angle 7 and angle 5 are consecutive interior angles on the same side of the transversal, so they are supplementary, not congruent: $\angle 5 + \angle 7 = 180^\circ$. - Angle 2 is top-right at line $m$ and $t$ intersection (top). Angle 7 and angle 2 are alternate exterior angles, so they are congruent: $\angle 2 = 75^\circ$. - Angle 6 is top-right at line $n$ and $t$ intersection (bottom). Angle 7 and angle 6 are vertical angles, so they are congruent: $\angle 6 = 75^\circ$. 5. **Conclusion:** The angle NOT congruent to angle 7 is angle 5. **Final answer:** Angle 5 is NOT congruent to angle 7.