1. **Problem statement:** Given two parallel lines AB and CD, and two intersecting lines creating angles 58° and 61° between them, find the measures of angles 1 and 2 formed at the upper parallel line AB. 2. **Key fact:** When two parallel lines are cut by a transversal, alternate interior angles are equal, and corresponding angles are equal. 3. **Identify angles:** The 58° angle is an alternate interior angle to angle 1, so angle 1 = 58°. 4. **Calculate angle 2:** Angles 1 and 2 are on a straight line at point B, so they are supplementary. 5. **Use supplementary angle rule:** $$\text{angle 1} + \text{angle 2} = 180^\circ$$ 6. Substitute angle 1: $$58^\circ + \text{angle 2} = 180^\circ$$ 7. Solve for angle 2: $$\text{angle 2} = 180^\circ - 58^\circ = 122^\circ$$ **Final answers:** - Angle 1 = 58° - Angle 2 = 122°