1. Problem: Find the missing right triangle number in a diamond where the center is 150, top is 100, bottom is 150, left is 150, and right is 50. Step 1: Understand that the center number is the sum of the left and right triangles. Step 2: Given center = 150, left = 150, solve for right: $$150 = 150 + \text{right} \Rightarrow \text{right} = 150 - 150 = 0$$ Step 3: The right triangle number is 50 as stated, so verify if center matches left + right: 150 = 150 + 50 = 200, which is not correct. Since the provided right value is 50 and center is 150, this is inconsistent. Usually, center = left + right. Assuming the problem asks to find consistency, the right triangle number should be: $$\text{right} = 150 - 150 = 0$$ 2. Problem: Find the missing right triangle number in a diamond where the center is 215, top is 150, bottom is 150, left is 200, and right is empty. Step 1: Center = left + right Step 2: Solve for right: $$215 = 200 + \text{right} \Rightarrow \text{right} = 215 - 200 = 15$$ 3. Problem: Find the center number in a diamond where top = 75, bottom = 75, left = 75, right = 75. Step 1: Center = left + right Step 2: Calculate: $$\text{center} = 75 + 75 = 150$$ 4. Problem: Find the center number in a diamond where top = 125, bottom = 200, left = 125, right = 150. Step 1: Center = left + right Step 2: Calculate: $$\text{center} = 125 + 150 = 275$$ 5. Problem: Find the missing right triangle number in a diamond where center is 75, top is 50, bottom is 50, left is 25, right is empty. Step 1: Center = left + right Step 2: Solve for right: $$75 = 25 + \text{right} \Rightarrow \text{right} = 75 - 25 = 50$$ 6. Problem: Find the missing right triangle number in a diamond where center is 105, top is 15, bottom is 75, left is 75, right is empty. Step 1: Center = left + right Step 2: Solve for right: $$105 = 75 + \text{right} \Rightarrow \text{right} = 105 - 75 = 30$$