Final answer:
WX is calculated by understanding that if T and V are midpoints of UX and UW, respectively, and TV = 40, then UT = TX = 40 and UV = VW = 80. Hence, WX is twice the length of VW, which is 160.
Step-by-step explanation:
The question asks us to determine the length of segment WX given that T is the midpoint of UX and V is the midpoint of UW, and that TV equals 40. If T is the midpoint of UX, then UT = TX. Similarly, if V is the midpoint of UW, then UV = VW.
Considering that T and V are points on the same line segment and that TV is a part of both UT and VW, we can understand that UT (which also equals TX since T is the midpoint) plus TV must equal UV. Since TV is given as 40, it means that UT = TX = 40. Now, UV = VW, but UV is comprised of UT + TV, which means UV and thus, VW is 40 + 40 = 80.
Therefore, we can conclude that WX, being the full length of UW, equals UV (or VW) times two, which gives us WX = 80 * 2 = 160.