By the Trapezoid Midsegment Theorem, the midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases.
YV and XW are the bases and GF is the midsegment. So:
[tex]\begin{gathered} GF=\frac{YV+XW}{2} \\ \text{this is } \\ 26=\frac{YV+24}{2} \end{gathered}[/tex]
And solve for YV:
[tex]\begin{gathered} 2\cdot26=2\cdot\frac{YV+24}{2}_{} \\ 52=YV+24 \\ 52-24=YV+24-24 \\ YV=28 \end{gathered}[/tex]
Answer: b. 28
