In the given figure, $ABCD$ is a parallelogram. $E$ and $F$ are points on opposite sides $AD$ and $BC$, respectively, such that $ED=\frac{1}{3}AD$ and $BF=\frac{1}{3}BC$.

If $\angle ADF=60°$, then find $\angle BFD$.

 

In a quadrilateral $ABCD, \angle B=130°, \angle C=60°$ and angle bisectors of $\angle A$ and $\angle D$ meet at $P$. Find $\angle APD$.

In the given figure, $PQRS$ is a parallelogram in which $PQ$ is produced to $T$, such that $QT=PQ$. Prove that $ST$ bisects $RQ$.

In figure below $PQRS$ is a parallelogram. $PO$ and $QO$ are respectively the angle bisectors of $\angle P$ and $\angle Q$. Line $LOM$ is drawn parallel to $PQ$. Prove that: $PL=QM$

In figure below $PQRS$ is a parallelogram. $PO$ and $QO$ are respectively the angle bisectors of $\angle P$ and $\angle Q$. Line $LOM$ is drawn parallel to $PQ$. Prove that: $LO=OM$