Question

Question was provided via image upload.

Explanation:

Step1: Identify the relationship

From the figure, we know that the length of segment $xz$ is 24 and the length of segment $yz$ is 8. We want to find the length of segment $xy$.

Step2: Use the segment - addition postulate

The segment - addition postulate states that if $y$ is between $x$ and $z$, then $xz=xy + yz$. Rearranging the formula to solve for $xy$, we get $xy=xz - yz$.

Step3: Substitute the given values

Substitute $xz = 24$ and $yz = 8$ into the formula $xy=xz - yz$. So, $xy=24 - 8$.

Step4: Calculate the result

$24-8 = 16$.

Answer:

16