1. **Stating the problem:** We are given two diagrams with marked angles at points P and Q. We need to identify angles that are alternate, cointerior, and corresponding to the marked angles. 2. **Important angle relationship rules:** - **Alternate angles:** Angles on opposite sides of the transversal and inside the two lines. - **Cointerior angles:** Angles on the same side of the transversal and inside the two lines, their sum is 180°. - **Corresponding angles:** Angles in the same relative position at each intersection where a transversal crosses two lines. 3. **Diagram 1 (angle ∠APF at P):** - i.a Alternate angle to ∠APF is ∠FQD (opposite side of transversal, inside lines). 4. **Diagram 1 (angle ∠FQD at Q):** - i.b Alternate angle to ∠FQD is ∠APF. 5. **Diagram 2 (angle ∠APB at P):** - ii.a Cointerior angle to ∠APB is ∠FQD (same side of transversal, inside lines). 6. **Diagram 1 (angle ∠FQD at Q):** - ii.b Cointerior angle to ∠FQD is ∠APB. 7. **Diagram 1 (angle ∠EPF at P):** - iii.a Corresponding angle to ∠EPF is ∠EQD (same relative position at intersections). 8. **Diagram 1 (angle ∠EQD at Q):** - iii.b Corresponding angle to ∠EQD is ∠EPF. **Final answers:** - i.a Alternate angle to ∠APF is ∠FQD. - i.b Alternate angle to ∠FQD is ∠APF. - ii.a Cointerior angle to ∠APB is ∠FQD. - ii.b Cointerior angle to ∠FQD is ∠APB. - iii.a Corresponding angle to ∠EPF is ∠EQD. - iii.b Corresponding angle to ∠EQD is ∠EPF.