In the adjacent figure $HOPE$ is a parallelogram. Find the angle measures $x, y \text{and} z$. State the geometrical truths you use to find them.

A circle is inscribed in quadrilateral ABCD, touching sides AB, BC, CD and DA at P, Q,R and S, respectively. If $\mathrm{As}=6\mathrm{cm},$ $\mathrm{BC}=12\mathrm{cm}$ and $\mathrm{CR}=5\mathrm{cm}$, then the length of AB (in cm) is

How many quadrilaterals are there in the given figure?

In the figure, $\mathrm{PQRS}$ and $\mathrm{ABCR}$ are two parallelograms. If $\angle \mathrm{P} = 110°$ then, find the measures of all angles of $\mathrm{ABCR}$.

In figure, $\mathrm{ABCD}$ is a parallelogram. Point$\mathrm{E}$ is on the ray $\mathrm{AB}$ such that $\mathrm{BE}=\mathrm{AB}$, then prove that line $\mathrm{ED}$ bisects segment $\mathrm{BC}$ at point $\mathrm{F}$.

Perimeter of a parallelogram is $150 \mathrm{cm}$. One of its sides is greater than the other side by $25 \mathrm{cm}$. Find the lengths of all sides.