check the picture below.
if VW ≅ VU, that simply means those two sides are twins, and twin sides, coming from a vertex at V like there, will make twin angles on the "base", of the isosceles triangle.
and since the angles are twins, then
[tex]\bf \stackrel{\measuredangle U}{8x-1}~~=~~\stackrel{\measuredangle W}{5x+23}\implies 3x=24\implies x=\cfrac{24}{3}\implies \boxed{x=8}\\\\
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\measuredangle W=5(8)+23[/tex]
