The adjacent angles of a quadrilateral are $60°$ and $130°$. Can the quadrilateral be a parallelogram? If so, why?

In the given figure, $PQRS$ is a parallelogram with $\angle SPQ=80°$ and $\angle SQR=45°$. Find the measure of $\angle RSQ$ and $\angle PSQ$.

In the given figure, $ABCD$ is a parallelogram with $\angle A=70°$. The bisectors of $\angle B$ and $\angle C$ meet at $P$ inside the parallelogram. Find the measure of $\angle BPC$.

In the given figure, $PQRS$ is a parallelogram. Find the value of $\angle x, \angle y,$ and $\angle z$.

In the adjacent figure, $ABCD$ is a parallelogram and line segments $AE$ and $CF$ bisect the angles $A$ and $C$ respectively. Show that $AE\parallel CF$.