1. **Problem Statement:** Identify the type of angle pairs for the given angle pairs in the diagram. 2. **Important Definitions:** - Corresponding angles: Angles in the same relative position at each intersection where a transversal crosses two lines. - Same-side interior angles: Angles on the same side of the transversal and inside the two lines. - Alternate interior angles: Angles on opposite sides of the transversal and inside the two lines. - Alternate exterior angles: Angles on opposite sides of the transversal and outside the two lines. 3. **Angle Pair Analysis:** - ∠2 and ∠7: These are on opposite sides of the transversal and outside the two lines, so they are **alternate exterior angles**. - ∠8 and ∠3: These are on the same side of the transversal and inside the two lines, so they are **same-side interior angles**. - ∠1 and ∠5: These are in the same relative position at each intersection, so they are **corresponding angles**. - ∠5 and ∠4: These are on opposite sides of the transversal and inside the two lines, so they are **alternate interior angles**. - ∠6 and ∠4: These are in the same relative position at each intersection, so they are **corresponding angles**. 4. **Summary of angle pairs:** - ∠2 and ∠7: Alternate exterior angles - ∠8 and ∠3: Same-side interior angles - ∠1 and ∠5: Corresponding angles - ∠5 and ∠4: Alternate interior angles - ∠6 and ∠4: Corresponding angles 5. **Drawing a Diagram (Problem 25):** - Draw trapezoid ABCD with \(\overrightarrow{AB} \parallel \overrightarrow{DC}\). - Draw line e intersecting trapezoid ABCD. - Label angles so that ∠1 and ∠6 are alternate exterior angles. - Label angles so that ∠2 and ∠3 are same-side interior angles. - Label angles so that ∠4 and ∠5 are supplementary to ∠3 (i.e., \(\angle4 + \angle3 = 180^\circ\) and \(\angle5 + \angle3 = 180^\circ\)). 6. **Real-world examples (Problem 26):** - Railroad tracks crossed by a road. - Window blinds with slats crossed by a string. - Two parallel shelves crossed by a vertical support. 7. **Map angle pairs (Problem 27):** - a. Town hall and gas station: Corresponding angles. - b. School and library: Alternate interior angles. - c. Library and post office: Same-side interior angles. - d. School and gas station: Alternate exterior angles. Final answers: - 20. ∠2 and ∠7: Alternate exterior angles - 22. ∠8 and ∠3: Same-side interior angles - 24. ∠1 and ∠5: Corresponding angles - 21. ∠5 and ∠4: Alternate interior angles - 23. ∠6 and ∠4: Corresponding angles