Free Quadrilaterals 02 Practice Test - 9th Grade 

A kite is a quadrilateral.
We know that, the sum of the angles of a quadrilateral is equal to 360°.
$\Rightarrow$ The sum of the angles of a kite is also equal to 360°.

A quadrilateral is a polygon with four sides and four vertices.

A quadrilateral has four sides, four angles and four vertices. Square, trapezium and rhombus are quadrilaterals. A circle can be approximated as a polygon with infinite sides but it is not a polygon. 

It is because a polygon must have straight edges (sides). A circle doesn't have straight sides.

A parallelogram is a quadrilateral whose both pairs of opposite sides are parallel. 

Sum of all angles of a quadrilateral is ${360}^{\circ }$.

$Fourthangle={360}^{\circ }-({75}^{\circ }+{90}^{\circ }+{75}^{\circ })={120}^{\circ }$

Since the pairs of opposite angles of a parallelogram are equal, this quadrilateral cannot be a parallelogram since it has three different angles and only one pair of equal angles.

Since ABEF is a parallelogram, so AF || BE and BF is the transversal.
$\therefore \angle AFB=\angle FBE=x$
$\text{[Alternate angles]}$

Also, since BCED is a parallelogram,
BE || CD and BD is the transversal.
$\therefore \angle CDB=\angle EDB=y$
$\text{[Alternate angles]}$ 

Now, 
$\angle FBD=\angle FBE+\angle EBD$ 
$\angle FBD=x+y$

And,
$\angle AFE=\angle BED$
$\text{[Corresponding angles]}$ 
$\therefore \angle AFE=z$ 

$\angle BED=\angle BCD=z$ 
$\text{[opposite angles of a parallelogram]}$

$\angle CDG+\angle BCD=\angle EBD+\angle BED$
$\text{[Sum of opposite interior angles is}\text{equal to exterior angle of a triangle]}$

$\Rightarrow \angle CDG=y+z-y$
$\Rightarrow \angle CDG=z$

Let the smallest angle of quadrilateral be $x^{\circ }$.
Then, the angles of the quadrilateral will be $x^{\circ }$, $2x^{\circ }$, $3x^{\circ }$ and $4x^{\circ }$.
Sum of the angles of a quadrilateral is ${360}^{\circ }$. 
$\Rightarrow {360}^{\circ }=x+2x+3x+4x$
$\Rightarrow 10x={360}^{\circ }$
$\therefore x={36}^{\circ },2x={72}^{\circ },3x={108}^{\circ }and4x={144}^{\circ }$

By joining the mid points of the sides of a quadrilateral, another quadrilateral is formed whose opposite sides will be equal and parallel. Hence the quadrilateral formed is a parallelogram.

A parallelogram is a quadrilateral whose both pairs of opposite sides are equal and parallel. Since the pairs of opposite sides equal and parallel in a square, rhombus and rectangle,  they are all parallelograms.

In a trapezium only one pair of opposite sides are parallel. 
In a parallelogram, both pairs of opposite sides are equal and parallel. 
Therefore a trapezium is not a parallelogram.