Explanation:
the sum of all angles in a triangle is always 180°.
so, the angle at T :
180 = 46 + 58 + angle T
angle T = 180 - 46 - 58 = 76°
and angle V :
180 = 46 + 76 + angle V
angle V = 180 - 46 - 76 = 58°
so, both triangles are similar, as all 3 pairs of corresponding angles are equal.
S corresponds to V.
T corresponds to W.
U corresponds to X.
therefore, there is one common (scaling) factor (f) for all pairs of sides.
WX corresponds to TU.
WV (37) corresponds to TS (74).
XV (x) corresponds to US.
so, it must be
TS × f = WV
74 × f = 37
f = 37/74 = 1/2
US × f = XV
100 × f = x
100 × ½ = x
50 = x
FYI : if you know trigonometric functions (sine, cosine, ...) already, then there would have been a direct approach (without needing the second triangle) by using the law of sine :
a/sinA = b/sinB = c/sinC
with a, b, c being the sides of the triangle, and A, B, C being the corresponding opposite angles.
37/sin(46) = x/sin(76)
x = 37×sin(76)/sin(46) = 49.90818227... ≈ 49.9 ≈ 50
that little difference to 50 just means that the angles (or the side lengths) were rounded in the graphic.