(Note: We have to assume PXT is a straight line segment or else it
couldn't be true.)

PLAN:
We only have to prove that all three triangles in the 
figure are right triangles which have their corresponding angles
congruent.  For then Angle S will be congruent to right Angles 
4 and 5. 

The "main" theorem we will use is:

If two angles of a triangle are congruent to two angles
of another triangle, then the third angles are also congruent.
  
Angles 4 and 5 are given as right angles and Angle 1 is 
Congruent to Angle 2.  Therefore by that "main" theorem above,
Angles P and Y are congruent.

Therefore Angle P and Angle T are congruent, for they are both
congruent to Angle Y.

Angles 1 and 3 are congruent because they are vertical angles.

Therefore by the "main" theorem above, Angles 4 and S are
congruent. 

Angle 4 is a right angle.

Therefore Angle S is also a right angle, and that proves that
ST is perpendicular to SY.

Edwin