1. **Problem Statement:** Find the sums of angle pairs given by: $$\angle 1 + \angle 5, \angle 2 + \angle 6, \angle 4 + \angle 8, \angle 3 + \angle 7$$ and identify pairs of interior angles on the same side of the transversal, and pairs of corresponding angles. 2. **Relevant Concepts:** - When two lines are cut by a transversal, certain angle pairs have special relationships. - **Corresponding angles** are equal. - **Interior angles on the same side of the transversal** are supplementary (sum to 180 degrees). 3. **Step-by-step solution:** **Step 1:** Identify angle pairs. - Given the diagram, angles numbered 1 to 8 are formed by two lines and a transversal. **Step 2:** Sum of angle pairs: - $$\angle 1 + \angle 5$$ are corresponding angles, so $$\angle 1 = \angle 5$$. - $$\angle 2 + \angle 6$$ are interior angles on the same side of the transversal, so $$\angle 2 + \angle 6 = 180^\circ$$. - $$\angle 4 + \angle 8$$ are corresponding angles, so $$\angle 4 = \angle 8$$. - $$\angle 3 + \angle 7$$ are interior angles on the same side of the transversal, so $$\angle 3 + \angle 7 = 180^\circ$$. **Step 3:** Pairs of interior angles on the same side of the transversal: - $$\angle 2 + \angle 6 = 180^\circ$$ - $$\angle 3 + \angle 7 = 180^\circ$$ **Step 4:** Pairs of corresponding angles: - $$\angle 6 + \angle 4$$ - $$\angle 5 + \angle 3$$ 4. **Summary:** - $$\angle 1 = \angle 5$$ - $$\angle 4 = \angle 8$$ - $$\angle 2 + \angle 6 = 180^\circ$$ - $$\angle 3 + \angle 7 = 180^\circ$$ - Corresponding angle pairs include $$\angle 6 + \angle 4$$ and $$\angle 5 + \angle 3$$. This completes the solution for the first question.