Answer:
m∠RPS = 38°.
Step-by-step explanation:
It is given that ray PT is the angle bisector of angle RPS. It means PT divides the angle RPS in two equal parts.
[tex]m\angle RPT=m\angle TPS=19^{\circ}[/tex]
Now, it is clear that
[tex]m\angle RPS=m\angle RPT+m\angle TPS[/tex]
[tex]m\angle RPS=19^{\circ}+19^{\circ}[/tex]
[tex]m\angle RPS=38^{\circ}[/tex]
Therefore, the measure of angle RPS is 38°.
