Diagonals of a quadrilateral $ABCD$ bisect each other. If $\angle A = 35^{\circ}$,determine $\angle B$. (in $^{\circ}$)

$P, Q, R$ and $S$ are respectively the mid-points of the sides $AB, BC, CD$ and $DA$ of a quadrilateral $ABCD$ such that $AC \perp BD$. Prove that $PQRS$ is a rectangle.

In quadrilateral $ABCD$,$\angle A : \angle B : \angle C : \angle D = 1 : 4 : 2 : 2$. Find the measure of each angle of the quadrilateral.

In $\Delta ABC$,$P, Q,$ and $R$ are the midpoints of $AB, BC,$ and $CA$ respectively. Prove that $PBQR, PQCR,$ and $PQRA$ all are parallelograms.

In $\Delta PQR$,$X, Y$ and $Z$ are the midpoints of $PQ, QR$ and $RP$ respectively. If $PQ = 7.2 \, cm$,$PR = 8.4 \, cm$ and $XZ = 3.8 \, cm$,then find the perimeter of $\Delta PQR$ and $\Delta XYZ$.

In the figure,$ABCD$ and $AEFG$ are two parallelograms. If $\angle C = 55^{\circ},$ determine $\angle F.$ (in $^{\circ}$)