Exercise 4 Page 37

We have been asked to find the measure of angle $RPT.$ The expression $m\angle RPT$ tells us to find the measure of the angle between rays $PR$ and $PT.$ Similarly, $m\angle RPB$ tells us to find the angle between rays $PR$ and $PB.$ Let's start by identifying the three angles.

It is given that $\overrightarrow{PB}$ is the angle bisector which means that it divides $\angle RPT$ into two congruent angles, $\angle RPB$ and $\angle BPT.$ Therefore the measures of $\angle RPB$ and $\angle BPT$ are equal.