This is a standard method; it is very direct and elegant. The new parallel line splits the given right-angle into two angles. These angles are equal to u and v [using the ‘alternate angles’ or ‘Z-angles’ property of parallel lines and a transversal].
Thus u + v = 90˚, or v = 90˚ – u.
So v = 70˚ when u = 20˚.

Note: As is common in geometry, the symbols u and v are being used in two ways simultaneously:
as names for angles and as numbers of degrees.