Prove diagonals of rhombus are perpendicular to each other.

In the given figure, $ABCD$ is a rhombus in which $\angle c=60°$, then $AC:BD$ will be

A rectangle with $12 \mathrm{cm}$ and $4 \mathrm{cm}$, reformed into a Rhombus. Both diagonals of Rhombus are equal and one of its angle is ${60}^{\mathrm{o}}$. Find the Area of Newly formed Rhombus.

Let $ABCD$ be a square. An arc of a circle with $A$ as centre and $AB$ as radius is drawn inside the square joining the points $B$ and $D$. Points $P$ on $AB, S$ on $AD, Q$ and $R$ on arc $BD$ are taken such that $PQRS$ is a square. Further suppose that $PQ$ and $RS$ are parallel to $AC$. Then, $\frac{\text{ area }PQRS}{\text{ area }ABCD}$ is

The angles of a quadrilateral are in the ratio $3:5:7:9$. Find the measure of each of these angles.

The three angles of a quadrilateral are $76°, 54° \mathrm{and} 108°$. Find the measure of the fourth angle.

The quadrilateral formed by angle bisectors of a cyclic quadrilateral is a

The angles of a quadrilateral are in the ratio $1:2:3:4$. Find the measure of each angle.