1. **Stating the problem:** We have two parallel lines cut by a transversal, creating several angles. We are asked to identify which two angles are corresponding and which two are alternate, given one angle measures 135°. 2. **Key concepts:** - Corresponding angles are pairs of angles that lie on the same side of the transversal and in corresponding positions relative to the parallel lines. - Alternate interior angles lie on opposite sides of the transversal and between the two parallel lines. - When two parallel lines are cut by a transversal, corresponding angles are equal, and alternate interior angles are equal. 3. **Given:** One angle measures 135°. 4. **Finding corresponding angles:** If angle G (on line A) is 135°, then the angle at Y (on line C) in the same relative position is also 135° because corresponding angles are equal. 5. **Finding alternate interior angles:** The angle alternate to 135° on the opposite side of the transversal and between the parallel lines is angle X or Z depending on the diagram. Since the transversal cuts the parallel lines, the alternate interior angle to 135° is 45° (because 180° - 135° = 45°). 6. **Summary:** - Corresponding angles: angle G and angle Y (both 135°). - Alternate interior angles: angle G and angle Z (or X), where angle Z (or X) = 45°. This uses the fact that angles on a straight line sum to 180°, and parallel lines create equal corresponding and alternate interior angles. **Final answer:** - Corresponding angles: G and Y - Alternate interior angles: G and Z