1. **Problem statement:** Given that the side of the house and the side of the shed are parallel, find the measures of angles $\angle 1$ and $\angle 2$ when one angle is given as 58°. 2. **Relevant formula and rules:** When two parallel lines are cut by a transversal, the consecutive interior angles (also called same-side interior angles) are supplementary. This means: $$\angle 1 + \angle 2 = 180^\circ$$ 3. **Given:** One angle is 58° (assume this is $\angle 1$). 4. **Calculate $\angle 2$:** $$\angle 2 = 180^\circ - \angle 1 = 180^\circ - 58^\circ = 122^\circ$$ 5. **Answer:** $$\angle 1 = 58^\circ, \quad \angle 2 = 122^\circ$$ These angles are supplementary because they lie on the same side of the transversal between the parallel lines.