Triangle RAQ is isosceles, so ∠R = ∠Q. The givens tell you the sides on either side of those angles are congruent, so TRA is SAS congruent to SQA. Corresponding angles of congruent triangles are equal, so ∠RAT = ∠QAS.
The process is
a) read and understand the problem statement
b) understand the given relationships and what that means for other relationships in the geometry
c) understand what you are asked to prove and how that relates to what is given and the postulates of geometry
