Three angles of a quadrilateral are $75^{\circ}, 90^{\circ}$ and $75^{\circ}$. The fourth angle is (in $^{\circ}$)

$P, Q, R$ and $S$ are respectively the mid-points of the sides $AB, BC, CD$ and $DA$ of a quadrilateral $ABCD$ in which $AC = BD$. Prove that $PQRS$ is a rhombus.

$E$ and $F$ are respectively the mid-points of the non-parallel sides $AD$ and $BC$ of a trapezium $ABCD$. Prove that $EF \parallel AB$ and $EF = \frac{1}{2}(AB + CD)$.

If $APB$ and $CQD$ are two parallel lines,then the bisectors of the angles $APQ, BPQ, CQP$ and $PQD$ form

In $\Delta PQR$,$A$,$B$,and $C$ are the mid-points of $PQ$,$QR$,and $RP$ respectively. If the perimeter of $\Delta ABC$ is $18.6 \, cm$,then the perimeter of $\Delta PQR$ is $\ldots \ldots \ldots cm$.

In a rhombus $ABCD$,if $AB = 13 \text{ cm}$,then the perimeter of $ABCD = \ldots \ldots \ldots \text{ cm}$.