Quadrilaterals Test

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Quadrilaterals Test - 17

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Weekly Quiz Competition

Question 1
1 / -0

Angles of a quadrilateral are in the ratio 3 : 6 : 8 : 13. The largest angle is :

A
$$178^{\circ}$$

B
$$90^{\circ}$$

C
$$156^{\circ}$$

D
$$36^{\circ}$$

Solution

Given ratio of angles are $$3 : 6 : 8 : 13$$.
Let the angles be $$3x$$ ,$$6x$$ ,$$8x$$ ,$$13x$$.

By angle sum property, the sum of all angles of quadrilateral is $$360^o.$$
So, $$3x+6x+8x+13x=360^o$$
$$\implies$$ $$30x=360^o$$
$$\implies$$ $$x=\dfrac{360^o}{30}$$
$$\implies$$ $$x=12^o$$.

Then,
$$3x=3\times12^o=36^o$$,
$$6x=6\times12^o=72^o$$,
$$8x=8\times12^o=96^o$$
and $$13x=13\times12^o=156^o$$.

Hence, the largest angle is $$156^o$$.
Therefore, option $$C$$ is correct.
Question 2
1 / -0

Which of the following is not a parallelogram ?

A
Rhombus

B
Rectangle

C
Trapezium

D
Square

Solution

Trapezium
Both trapezium and parallelogram are quadrilaterals. A parallelogram has two pairs of parallel sides. A trapezoid only has one pair of parallel sides.
Hence, the answer is Trapezium.
Question 3
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Which of the following pair of shapes when joined together (by placing from edge to edge) can form a rectangle?

A

B

C

D
None of these

Solution

Properties of rectangle are :
$$\Rightarrow$$ Each of the interior angles is 90$$^\circ$$.
$$\Rightarrow$$ Opposite sides of rectangle are parallel.
$$\Rightarrow$$ Opposite sides of rectangle are equal.
$$\Rightarrow$$ So, by joining pair of shapes of option B and C we will not form rectangle because they are not satisfying all the properties of rectangle.
$$\Rightarrow$$ So, only joining pair of shapes of option A, can form a rectangle because it's satisfy all the properties of rectangle.
Question 4
1 / -0

Each angle of a square is of measure ___ .

A
$$\displaystyle 30^{\circ}$$

B
$$\displaystyle 45^{\circ}$$

C
$$\displaystyle 60^{\circ}$$

D
$$\displaystyle 90^{\circ}$$

Solution

Each angle of a square is of measure $$ {90}^{o} $$
Question 5
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A quadrilateral has ______ diagonals.

A
1

B
4

C
2

D
3

Solution

We know that, a quadrilateral is a $$4-sided$$ geometrical figure.
It has $$4$$ vertices.
Hence, there are only $$2$$ pairs of opposite (non-adjacent) vertices in a quadrilateral.
We also know that, a diagonal is a line segment joining two opposite (non-adjacent) vertices.

Therefore, a quadrilateral has $$2$$ diagonals.
Question 6
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Complete the following statement.
Number of measurements required to construct a square are__________.

A
1

B
2

C
3

D
4

Solution

If we know the length of the side of the square, we can construct it since a square has all four sides equal and each of the four angles is equal to $$ {90}^{o} $$

Hence, number of measurements required to construct a square is $$ 1 $$
Question 7
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Number of pairs of parallel lines in a trapezium is:

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

A trapezium has one pair of parallel lines as shown in the figure. So option $$A$$ is correct.
Question 8
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Which of the following are equiangular and equilateral polygons?

A
Square

B
Rhombus

C
Kite

D
None of these

Solution

Squares are equiangular and equilateral polygons as it has all the sides and angles equal.
Question 9
1 / -0

The angle of a quadrilateral are respectively $$120^o, 73^o, 80^o$$. Find the fourth angle.

A
$$87^o$$

B
$$85^o$$

C
$$67^o$$

D
$$57^o$$

Solution

Let the four angles be $$ \angle A , \angle B , \angle C$$ and $$\angle D$$ .

Then $$ \angle A =120^o, \angle B=73^o , \angle C = 80^o $$ .

We know, by angle sum property, the sum of angles of a quadrilateral is $$360^o$$.
$$\implies$$ $$ \angle A + \angle B + \angle C + \angle D = 360^{o} $$.

Then, $$ \angle D $$ will be given by:

$$\angle D = 360^o - \angle A - \angle B-\angle C $$

$$ \Rightarrow \angle D = 360 ^o-120^o -73^o -80^o $$

$$ \Rightarrow \angle D = 360 - 273^o$$
$$ \Rightarrow \angle D = 87^o$$.

The measure of fourth angle is $$ 87 ^{o}$$.

Therefore, option $$A$$ is correct.
Question 10
1 / -0

Find the angle measure x in the following figures

A
$$60^o$$

B
$$50^o$$

C
$$70^o$$

D
$$80^o$$

Solution

Since the sum of angles (interior angles) of a quadrilateral is $$360^o$$.
$$\therefore x + 120^o + 130^o + 50^o = 360^o$$
$$\Rightarrow x + 300^o = 360^o$$
$$\Rightarrow x= 360^o-300^o = 60^o$$