#### Answer

XY=21
YZ=29

#### Work Step by Step

Use the Segment Addition Postulate to find the value of a.
$XY+YZ=XZ$
substitute
$a+(a+8)=50$
combine like terms
$2a+8=50$
subtract 8 from each side
$2a+8-8=50-8$
simplify
$2a=42$
divide each side by 2
$2a\div2=42\div2$
$a=21$
Use the value of a to find the segment lengths.
$XY=a=21$
$YZ=a+8=21+8=29$