1. **Stating the problem:** We are given a transversal line $t$ intersecting two diagonal lines, creating eight angles numbered 1 to 8. We need to identify pairs of angles for three cases: a) Alternate interior angles b) Corresponding angles c) Interior angles on the same side of the transversal 2. **Recall definitions:** - **Alternate interior angles:** Angles on opposite sides of the transversal and inside the two lines. - **Corresponding angles:** Angles in the same relative position at each intersection. - **Interior angles on the same side of the transversal:** Angles inside the two lines and on the same side of the transversal. 3. **Analyze the diagram based on the description:** - The transversal $t$ is vertical. - Angles 1 and 2 are on the left diagonal line intersection. - Angles 5 and 6 are on the right diagonal line intersection. - Angles 3, 4, 7, 8 are on the transversal line $t$. 4. **Find alternate interior angles:** - Alternate interior angles are pairs like $\angle 2$ and $\angle 7$, $\angle 3$ and $\angle 6$. - So the pairs are $\angle 2 + \angle 7$ and $\angle 3 + \angle 6$. 5. **Find corresponding angles:** - Corresponding angles are pairs like $\angle 1$ and $\angle 5$, $\angle 2$ and $\angle 6$, $\angle 4$ and $\angle 8$, $\angle 3$ and $\angle 7$. 6. **Find interior angles on the same side of the transversal:** - These are pairs like $\angle 2$ and $\angle 6$, $\angle 3$ and $\angle 7$. **Final answers:** - a) Alternate interior angles: $\angle 2 + \angle 7$, $\angle 3 + \angle 6$ - b) Corresponding angles: $\angle 1 + \angle 5$, $\angle 2 + \angle 6$, $\angle 4 + \angle 8$, $\angle 3 + \angle 7$ - c) Interior angles on the same side of the transversal: $\angle 2 + \angle 6$, $\angle 3 + \angle 7$