When one is stuck, a good strategy is to ‘doodle’.
Here, one of the given lines has been extended to produce a triangle.
It turns out that we know its angles: u [given], v [alternate angles] and
90˚ [angles on a straight line].
Thus u + v + 90˚ = 180˚ [interior angle sum of triangle], so v = 90˚ – u.

In a sense, this is less direct than Method 1. If we think of geometry as a logically ordered system, then ‘angle sum of triangle’ is based on angle properties of parallel lines. For the above triangle, one standard angle-sum proof involves drawing the line constructed in Method 1!