1. We are given a square with center 150, top 100, left 150, right 50, bottom 150. To verify, note the center should be the average of left and right, and top and bottom. Calculate center x: $\frac{\text{left} + \text{right}}{2} = \frac{150 + 50}{2} = \frac{200}{2} = 100$. Given center x is 150, mismatch means an error in given data or it might be a test of finding missing values. 2. Square with center 215, top 150, left 200, right unknown, bottom 150. Find right using center x formula: $215 = \frac{200 + \text{right}}{2}$ $\Rightarrow 430 = 200 + \text{right}$ $\Rightarrow \text{right} = 230$ 3. Square with center unknown, top 75, left 75, right 75, bottom 75. Since left = right = 75, center x = $\frac{75 + 75}{2} = 75$. Similarly, top = bottom = 75, center y = $\frac{75 + 75}{2} = 75$. So center = 75. 4. Square with center unknown, top 125, left 125, right 150, bottom 200. Center x = $\frac{125 + 150}{2} = \frac{275}{2} = 137.5$ Center y = $\frac{125 + 200}{2} = \frac{325}{2} = 162.5$ 5. Square with center 75, top 50, left 25, right 50, bottom unknown. Center y = 75, top = 50, Find bottom using center y formula: $75 = \frac{50 + \text{bottom}}{2}$ $150 = 50 + \text{bottom}$ $\text{bottom} = 100$ 6. Square with center 105, top 15, left unknown, right 75, bottom 75. Center x = 105, right = 75, Find left using: $105 = \frac{\text{left} + 75}{2}$ $210 = \text{left} + 75$ $\text{left} = 135$ Summary answers: 1. Center x does not match horizontal middle; possibly data mismatch. 2. Right = 230 3. Center = 75 4. Center = (137.5, 162.5) 5. Bottom = 100 6. Left = 135