1. **State the problem:** We have two similar quadrilaterals. The first has angles 45°, 135°, 135°, and 45°. We need to find the missing angle in the second similar figure. 2. **Recall the property of similar figures:** Corresponding angles in similar figures are equal. 3. **Identify corresponding angles:** Since the figures are similar, each angle in the second figure matches the corresponding angle in the first figure. 4. **Use the given angles:** The first figure's angles are 45°, 135°, 135°, and 45°. The missing angle corresponds to one of these. 5. **Conclusion:** The missing angle is 45° because it corresponds to the 45° angle in the first figure. **Final answer:** The missing angle is **45°**.