Question

In parallelogram PQRS, QP is extended to point Iand ST is drawnPIf ST = SP and mZR = 130°, what is mZPST?

Answer 1

$\begin{gathered} m\angle R=130 \\ so\colon \\ m\angle P=130 \end{gathered}$$\begin{gathered} m\angle SPT=180-m\angle P \\ \text{Because they are supplementary} \\ m\angle SPT=180-130=50 \end{gathered}$$\begin{gathered} m\angle PTS=m\angle SPT \\ \text{Because:} \\ ST\cong SP \\ \text{Therefore:} \\ m\angle PST=180-m\angle PTS-m\angle SPT \\ m\angle PST=180-50-50 \\ m\angle PST=80 \end{gathered}$