In quadrilateral $ABCD$,$\angle A + \angle D = 180^{\circ}$. What special name can be given to this quadrilateral?

The perimeter of a rhombus is $100\,cm$ and one of its diagonals measures $48\,cm$. Then,the length of the other diagonal is ....... $cm.$

State whether each of the following statements is true or false:
$(1)$ $ABCD$ is a rhombus. If $AB = 12 \, \text{cm}$, then the perimeter of $ABCD$ is $48 \, \text{cm}$.
$(2)$ $PQRS$ is a square. If $PR = 8 \, \text{cm}$, then the perimeter of $PQRS$ is $32 \, \text{cm}$.

In trapezium $ABCD$,$AB \parallel CD$. If $\angle A = 70^{\circ}$ and $\angle B = 85^{\circ}$,then $\angle D = \ldots$ (in $^{\circ}$)

$P$ and $Q$ are points on opposite sides $AD$ and $BC$ of a parallelogram $ABCD$ such that $PQ$ passes through the point of intersection $O$ of its diagonals $AC$ and $BD$. Show that $PQ$ is bisected at $O$.

The angle between two altitudes of a parallelogram drawn from the vertex of an obtuse angle is $60^{\circ}$. Find the angles of the parallelogram.