## Geometry: Common Core (15th Edition)

$m\angle RPT=20$
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: $m\angle RPT=(8+2)+(2(8)-6)=10+10=20$