Triangles UTR and RTS are congruent, because they're both right triangles, RS=RU and side TR is in common.
This implies that angles RTS and RTU are congruent, and thus we have
[tex]5w-69=w+3 \iff 4w=72 \iff w=\dfrac{72}{4}=18[/tex]
Finally, angle STU is the sum of RTS and RTU, which is the same as 2RTU, since they have the same measure. So, we have
[tex]RTS+RTU=2RTU=2(w+3)=2w+6[/tex]
and since w=18, we have
[tex]2w+6=2\cdot 18+6=36+6=42[/tex]
