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

In $\Delta ABC$,$P$,$Q$,and $R$ are the midpoints of the sides. If the perimeter of $\Delta ABC$ is $23 \, cm$,then find the perimeter of $\Delta PQR$ in $cm$.

Show that the quadrilateral formed by joining the mid-points of the consecutive sides of a square is also a square.

Can the angles $110^{\circ}, 80^{\circ}, 70^{\circ}$ and $95^{\circ}$ be the angles of a quadrilateral? Why or why not?

$D, E$ and $F$ are respectively the mid-points of the sides $AB, BC$ and $CA$ of a triangle $ABC$. Prove that by joining these mid-points $D, E$ and $F$,the triangle $ABC$ is divided into four congruent triangles.

In $\Delta ABC$,$P$ and $Q$ are the midpoints of $AB$ and $AC$ respectively. If $PQ + BC = 8.4 \, cm$ and $AB + AC = 20.5 \, cm$,then find the perimeter of $\Delta ABC$ in $cm$.