Two adjacent angles of a parallelogram are in the ratio $4:5$. Find the measure of each of its angles.

Two adjacent angles of a parallelogram are $(3x-4)°$ and $(3x+16)°$. Find the value of $x$ and hence find the measure of each of its angles.

The sum of two opposite angles of a parallelogram is $130°$. Find the measure of each of its angles.

Two sides of a parallelogram are in the ratio $5:3$. If its perimeter is $64 \mathrm{cm}$, find the lengths of its sides.

The perimeter of a parallelogram is $140 \mathrm{cm}$. If one of the sides is longer than the other by $10 \mathrm{cm}$, find the length of each of its sides.

In the adjacent figure, $ABCD$ is a rectangle. If $BM$ and $DN$ are perpendiculars from $B$ and $D$ on $AC$, prove that $△BMC\cong △DNA$. Is it true that $BM=DN$?

In the adjacent figure, $ABCD$ is a parallelogram and line segments $AE$ and $CF$ bisect the angles $A$ and $C$ respectively. Show that $AE\parallel CF$.

The lengths of the diagonals of a rhombus are $16 \mathrm{cm}$ and $12 \mathrm{cm}$ respectively. Find the length of each of its sides.

In the given figure, $ABCD$ is a square. Find the measure of $\angle CAD$.