Final answer:
To find CD, we can set up the equation BC = CD and substitute the known values. Solving for x and substituting it back, we find that CD = 8.
Step-by-step explanation:
Let's use the fact that C is the midpoint of BD. This means that BC is equal to CD. So we can set up the equation BC = CD. We know that BC = x + 7 and CD = 8x. Substituting these values into the equation, we get x + 7 = 8x. Solving for x, we subtract x from both sides and subtract 7 from both sides to get 7 = 7x. Dividing both sides by 7, we get x = 1. Now we can find CD by substituting x = 1 into the equation CD = 8x. So CD = 8(1) = 8.