More algebra pretending to be geometry. What a waste.
The corresponding sides have to be congruent so this is a linear system with two equations in two unknowns,
8v - 4u + 28 = u + v
v + 2u + 26 = 17v - 3u
7v - 5u + 28 = 0
-16v + 5u + 26 = 0
Adding equations,
-9v + 54 = 0
-9v = -54
v = 6
5u = 7v + 28 = 42 + 28 = 70
u = 14
Answer: u=14, v=6
Check:
8v - 4u + 28 = 8(6) - 4(14) + 28 = 20
u + v = 14 + 6 = 20, good
v + 2u + 26 = 6 + 2(14) + 26 = 32+28 = 60
17v - 3u = 17(6) - 3(14) = 6(17- 7) = 60, good