In the figure given below, $ABCD$ is a rhombus. Find the value of $x$ and $y$.

In the figure given below, $ABCD$ is a rectangle. Find the values of $x°$ and $y°$ in each case.

In the figure given below, $ABCD$ is a rectangle. Find the values of $x°$ and $y°$ in each case.

In the adjoining figure, $\mathrm{ABCD}$ is a square. A line segment $\mathrm{CX}$ cuts $\mathrm{AB}$ at $\mathrm{X}$ and the diagonal $\mathrm{BD}$ at $\mathrm{O}$ such that $\angle \mathrm{COD}=80°$ and $\angle \mathrm{OXA}=x°$. Find the value of $x$.

In a parallelogram $ABCD$, points $M$ and $N$ have been taken on opposite sides $AB$ and $CD$ respectively such that $AM=CN$. Show that $AC$ and $MN$ bisect each other.