1. **State the problem:** We have a right triangle with two 45° angles and one leg of length $\sqrt{2}$. We need to find the hypotenuse $x$. 2. **Recall the properties of a 45°-45°-90° triangle:** In such a triangle, the legs are congruent, and the hypotenuse is $\sqrt{2}$ times the length of each leg. 3. **Write the formula:** $$x = \text{leg} \times \sqrt{2}$$ 4. **Substitute the known leg length:** $$x = \sqrt{2} \times \sqrt{2}$$ 5. **Simplify the expression:** $$x = \sqrt{2} \times \sqrt{2} = \sqrt{2 \times 2} = \sqrt{4} = 2$$ 6. **Conclusion:** The hypotenuse $x$ is 2.