1. **Problem statement:** We have a right triangle with angles 90° and 45°, and the side opposite the 45° angle is 12 cm. We need to find the missing side $x$, which is adjacent to the 45° angle. 2. **Formula and rules:** In a right triangle with a 45° angle, the triangle is isosceles, meaning the two legs are equal in length. The sides opposite the 45° angles are equal. 3. **Step-by-step solution:** Since the side opposite the 45° angle is 12 cm, the adjacent side $x$ is also 12 cm because in a 45°-45°-90° triangle, the legs are equal. 4. **Final answer:** $$x = 12\text{ cm}$$ This is because the legs opposite the 45° angles in a right isosceles triangle are equal.