1. **Problem:** Determine whether each pair of angles is True (T) or False (F) based on their relationship in the figure with two parallel lines and a transversal. 2. **Key angle relationships:** - Vertical angles are opposite angles formed by two intersecting lines and are always equal. - Alternate exterior angles lie outside the parallel lines on opposite sides of the transversal and are equal. - Corresponding angles are in the same relative position at each intersection of the transversal with the parallel lines and are equal. - Alternate interior angles lie between the parallel lines on opposite sides of the transversal and are equal. 3. **Evaluate each pair:** 1. ∠6 and ∠8: These are on the same side of the transversal but both on the bottom line, adjacent angles, not vertical. **False (F)** 2. ∠2 and ∠6: ∠2 is on the top line outside the parallel lines, ∠6 is on the bottom line outside the parallel lines, opposite sides of transversal. These are alternate exterior angles. **True (T)** 3. ∠1 and ∠3: Both on the top line, adjacent but not opposite angles. Not vertical. **False (F)** 4. ∠7 and ∠3: ∠7 is on bottom line, right side; ∠3 is on top line, left side. They are corresponding angles (same relative position). **True (T)** 5. ∠6 and ∠4: ∠6 is bottom line left side; ∠4 is top line right side. Not corresponding (corresponding angles are same side). **False (F)** 6. ∠3 and ∠5: ∠3 is top line left side; ∠5 is bottom line left side. Both inside parallel lines, opposite sides of transversal. Alternate interior angles. **True (T)** 7. ∠5 and ∠1: ∠5 bottom line left side; ∠1 top line right side. Not alternate interior (same side). **False (F)** 8. ∠2 and ∠8: ∠2 top line right side; ∠8 bottom line right side. Not vertical (vertical angles are opposite at intersection). **False (F)** **Final answers:** 1. F 2. T 3. F 4. T 5. F 6. T 7. F 8. F