1 Answer

Roger Willcocks · Answer 1 · 2020-08-19T17:28:32+0000

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

$5w-69=w+3 \iff 4w=72 \iff w=(72)/(4)=18$

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

RTS+RTU=2RTU=2(w+3)=2w+6

and since w=18, we have

$2w+6=2\cdot 18+6=36+6=42$

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