Let c = angle TPS
This angle adds to angle 'a' to get a+c = 90. We know these angles are complementary because triangle PQR is a right triangle. The acute angles of a right triangle add to 90.
We also know that b+c = 90 for similar reasons. Triangle PST is a right triangle.
So we have these two equations
a+c = 90
b+c = 90
If we were to subtract straight down then we would end up with
a-b = 0
which solves to
a = b
after adding b to both sides