1. **Stating the problem:** We have a polygon transformed by the rule $(x,y) \to (x, y - 8)$. We are given that the area of the new polygon is $\frac{1}{8}$ the area of the original polygon, the sum of the angle measures remains the same, the side lengths of the new polygon are each 8 units less than the original, and the angles of the new polygon are less than the original polygon's corresponding angles. 2. **Analyzing the transformation:** The transformation $(x,y) \to (x, y - 8)$ is a vertical translation downward by 8 units. A translation does not change the shape or size of a polygon, so the area and side lengths should remain the same, and angles should be unchanged. 3. **Checking the given statements:** - Area: Translation preserves area, so the area of the new polygon should be equal to the original polygon's area, not $\frac{1}{8}$ of it. - Sum of angle measures: This is always $180(n-2)$ degrees for an $n$-sided polygon, so it remains the same. - Side lengths: Translation does not change side lengths, so they should be equal, not 8 units less. - Angles: Translation does not change angles, so they should be equal, not less. 4. **Conclusion:** The statements about area being $\frac{1}{8}$, side lengths being 8 units less, and angles being less are incorrect for a translation. Only the sum of angle measures remains the same. **Final answer:** The only true statement is that the sum of the angle measures of the new polygon equals that of the original polygon. The other statements contradict the properties of translation.