In a parallelogram $ABCD$,$\angle A = 5x - 40^{\circ}$ and $\angle C = 3x + 10^{\circ}$,then $x = \ldots$

Opposite angles of a quadrilateral $ABCD$ are equal. If $AB = 4 \, cm$,determine $CD$ (in $cm$).

$ABCD$ is a parallelogram. If its diagonals are equal,then find the value of $\angle ABC$. (in $^{\circ}$)

In parallelogram $ABCD$,$\angle A = \angle B - 30^{\circ}$,then find $\angle A$. (in $^{\circ}$)

Diagonals $AC$ and $BD$ of a parallelogram $ABCD$ intersect each other at $O$. If $OA = 3\, cm$ and $OD = 2\, cm$,determine the lengths of $AC$ and $BD$.

In parallelogram $PQRS$,$PQ = 8 \, \text{cm}$ and $QR = 5 \, \text{cm}$,then the perimeter of $PQRS = \ldots \ldots \ldots$ (in $, \text{cm}$)