Define the terms: $\left(\mathrm{i}\right)$ Open curve $\left(\mathrm{ii}\right)$ Closed curve $\left(\mathrm{iii}\right)$ Simple closed curve

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

Two adjacent angles of a parallelogram are the ratio $2:3$. Find the measure of each of its angles.

The sides of rectangle are in the ratio $4:5$ and its perimeter is $180 \mathrm{cm}$. Find its sides.

Prove that the diagonals of a rhombus bisect each other at right angles.

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