The diagonals of a rectangle $ABCD$ intersect at a point $O$. If $\angle COD=78°$, then find the value of $\angle OAB$.

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: $LO=OM$

In the given figure, it is given that $BDEF$ and $FDCE$ are parallelograms. If $BD=8 \mathrm{cm}$, then determine $CD$.