1. **Problem Statement:** We have three parallel roads intersected by a transversal road, creating several angles. Given that \(\angle EBC = x^\circ\), we need to find the measures of related angles based on properties of parallel lines and transversals. 2. **Key Properties:** - Corresponding angles are equal. - Alternate interior angles are equal. - Consecutive interior angles (same side interior) are supplementary, summing to 180°. 3. **Step 1: Find \(\angle BED\) given \(\angle EBC = x^\circ\).** - \(\angle EBC\) and \(\angle BED\) are vertical angles formed by the intersection at point B and E respectively. - Vertical angles are equal. - Therefore, \(\angle BED = x^\circ\). 4. **Step 2: Find the angle equal to \(\angle HEF\).** - \(\angle HEF\) is on the middle road at point E. - Since the roads are parallel and cut by a transversal, \(\angle HEF\) corresponds to \(\angle EBC\) on the left road. - Corresponding angles are equal. - Therefore, \(\angle HEF = x^\circ\). 5. **Step 3: Find the angle supplementary to \(\angle GHE\).** - \(\angle GHE\) is on the right road at point H. - The angle supplementary to \(\angle GHE\) is \(\angle EHF\) on the same transversal side. - Consecutive interior angles sum to 180°. - Therefore, \(\angle GHE + \angle EHF = 180^\circ\). **Final answers:** - \(\angle BED = x^\circ\) - \(\angle HEF = x^\circ\) - \(\angle GHE + \angle EHF = 180^\circ\)