Explain how a square is a rhombus.

In a rhombus $ABCD, \angle CBA=40°$. Find the other angles.

The adjacent angles of a parallelogram are $x°$ and $(2x+30)°$. Find all the angles of the parallelogram. 

Explain how $DEAR$ is a trapezium. Which of its two sides are parallel? 

$BASE$ is a rectangle. Its diagonals intersect at $O$. Find $x$, if $OB=5x+1$ and $OE=2x+4$.

Is quadrilateral $ABCD$ a parallelogram, if $\angle A=70°$ and $\angle C=65°$? Give reason. 

Two adjacent sides of a parallelogram are in the ratio $5:3$ and the perimeter of the parallelogram is $48 \mathrm{cm}$. Find the length of each of its sides. 

The diagonals of the quadrilateral are perpendicular to each other. Is such a quadrilateral always a rhombus? Draw a rough figure to justify your answer.