1. **Problem Statement:** We have three parallel roads cut by a transversal road, creating several angles at intersections. We want to analyze the relationships between these angles. 2. **Key Concepts:** When a transversal crosses parallel lines, several angle relationships hold: - Corresponding angles are equal. - Alternate interior angles are equal. - Consecutive interior angles are supplementary (sum to 180°). 3. **Given:** If \(\angle EBC = x^\circ\), then \(\angle BED = x^\circ\). - These two angles are corresponding angles formed by the transversal and parallel lines, so they are equal. 4. **Given:** \(\angle HEF\) has the same measure as \(\angle ABE\). - These are alternate interior angles between the first and third parallel roads, so they are equal. 5. **Given:** The sum of \(\angle GHE\) and \(\angle EHI\) is 180°. - These two angles are consecutive interior angles on the same side of the transversal, so their measures add up to 180°. **Final answers:** - \(\angle EBC = \angle BED = x^\circ\) - \(\angle HEF = \angle ABE\) - \(\angle GHE + \angle EHI = 180^\circ\) These results follow from the properties of angles formed by a transversal crossing parallel lines.