Answer
$m\angle RPT=20$
Work Step by Step
SInce $\overset\longrightarrow{PB}$ bisects $\angle RPT$, $\angle RPB$ and$\angle TPB$ are congruent.
The measures of congruent angles are equal.
$x+2=2x-6$
Subtract x from each side.
$x+2-x=2x-6-x$
$2=x-6$
Add 6 to each side.
$2+6=x-6+6$
$8=x$
Angle Addition Postulate:
$m\angle RPT=m\angle RPB+m\angle TPB$
Substitute the given values:
$m\angle RPT=(x+2)+(2x-6)$
Substitute for x and simplify:
$m\angle RPT=(8+2)+(2(8)-6)=10+10=20$
