$\mathrm{ABCD}$ is a rhombus. Find each of the angles $x, y$ and $z$

$\mathrm{ABCD}$ is a rhombus. Consider $∆\mathrm{AOB}.$ What kind of triangle is $∆\mathrm{AOB}$?

$\mathrm{ABCD}$ is a rhombus. If $\mathrm{AO}=8 \mathrm{cm}$ and $\mathrm{BO}=6 \mathrm{cm}$, find $\mathrm{AB}$

$\mathrm{ABCD}$ is a rhombus. What is the length of each side of the rhombus? $\left(\mathrm{AO} = 8 \mathrm{cm} \mathrm{and} \mathrm{BO} = 6 \mathrm{cm}\right)$

$\mathrm{RENT}$ is an isosceles trapezium such that $\mathrm{TN}=15 \mathrm{cm}, \mathrm{TR}=7 \mathrm{cm}$ and the length between parallel sides is $6 \mathrm{cm}$. If the length of $\mathrm{RE}$ is $a-2\sqrt{b} cm.$ Find $a$.

$\mathrm{ABCD}$ is a rectangle and diagonals intersect each other at $\mathrm{O}$. If $\angle \mathrm{COD}=120°$, find $\angle \mathrm{ABO}$

$\mathrm{ABCD}$ is a rectangle and diagonals intersect each other at $\mathrm{O}$. If $\angle \mathrm{COD}=120°$, find $\angle \mathrm{ADO}$

$\mathrm{ABCD}$ is a rectangle and diagonals intersect each other at $O$. If $\angle \mathrm{COD}=120°$, find $\angle \mathrm{BCO}$

In a rhombus $\mathrm{ABCD}$, find $x, y$ and $z$. Hence, find the perimeter of the rhombus.