Answer:
Given
[tex]\triangle PST \cong \triangle RST[/tex]
Whenever we have a congruence between triangles, we can automatically conclude several congruence between their corresponding parts, that is called Corresponding Parts of Congruent Triangles are Congruent (CPCTC).
To determine the proper congruence with CPCTC, we need to respect the position of each vertex of the congruence expression, because the same positions indicates congruence.
In this case, to demonstrate [tex]\angle PTQ \cong \angle RTQ[/tex] we must use the following equivalence
[tex]\angle PTS \cong \angle RTS[/tex]
But, by supplementary angles, we have
[tex]\angle PTS + \angle PTQ = 180\°[/tex] and [tex]\angle RTS + \angle RTQ = 180\°[/tex]
As you can observe, these equations are congruent.
[tex]\angle PTS + \angle PTQ = \angle RTS + \angle RTQ[/tex]
Using the congruente: [tex]\angle PTS \cong \angle RTS[/tex]
[tex]\angle PTQ = \angle RTQ[/tex]
Therefore, the congrence between the given angles is true.
