M.C.Q. [1 Marks Each]

MCQ 11 Mark

$\text{PQRS}$ is a trapezium in which $PQ \| SR$ and $\angle\text{P}=130^\circ , \angle\text{Q}=110^\circ .$ Then $\angle\text{R}$ is equal to:

✓
$70^\circ$
B
$50^\circ$
C
$65^\circ$
D
$55^\circ$

Answer

Correct option: A.

$70^\circ$

Since, $\text{PQRS}$ is a trapezium and $PQ \| SR$
$\therefore\angle\text{Q}+\angle\text{R}=180^\circ$
$\Rightarrow\angle\text{R}= 180^\circ − 110^\circ$
$= 70^\circ$

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MCQ 21 Mark

The number of sides of a regular polygon whose each interior angle is of $135^\circ $ is:

A
$6$
B
$7$
✓
$8$
D
$9$

Answer

Correct option: C.

$8$

We know that, the measures of each exterior angle of a polygon having n sides is given by $\frac{360^\circ}{\text{n}}$
$\therefore$ The number of sides, $\text{n}=\frac{360^\circ}{\text{Exterior angle}}=\frac{360^\circ}{180^\circ}=\frac{360^\circ}{45^\circ}=8$

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MCQ 31 Mark

How many non-overlapping triangles can we make in a n-gon (polygon having n sides), by joining the vertices?

A
$n - 1$
✓
$n - 2$
C
$n - 3$
D
$n - 4$

Answer

Correct option: B.

$n - 2$

The number of non-overlapping triangles in a n-gon $= n - 2$, i.e., $2$ less than the number of sides.

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MCQ 41 Mark

Length of one of the diagonals of a rectangle whose sides are $10 \ cm$ and $24\ cm$ is.

A
$25\ cm$
B
$20\ cm$
✓
$26\ cm$
D
$3.5\ cm$

Answer

Correct option: C.

$26\ cm$

In $\triangle\text{BDC}=90^\circ$
Using Pythagoras Theorem, We have,
$\text{BC}^2=\text{BD}^2+\text{CD}^2$
$\Rightarrow\text{BC}^2=10^2+24^2=100+576$
$\Rightarrow\text{BC}^2=676$
$\Rightarrow\text{BC}=\sqrt{676}$
$\Rightarrow\text{BC}=256\text{cm}$

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MCQ 51 Mark

A quadrialateral whose opposite sides and all the angles are equal is a.

✓
rectangle
B
parallelogram
C
square
D
rhombus

Answer

Correct option: A.

rectangle

We know that, in a rectangle, opposite sides and all the angles are equal.

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MCQ 61 Mark

The sum of angles of a concave quadrilateral is:

A
more than $360^\circ$
B
less than $360^\circ$
✓
equal to $360^\circ$
D
twice of $360^\circ$

Answer

Correct option: C.

equal to $360^\circ$

We know that, the sum of interior angles of any polygon $($convex or concave$)$ having $n$ sides is $(n − 2) \times 180^\circ$
$\therefore$ The sum of angles of a concave quadrilateral is $(4 – 2) \times 180^\circ$, i.e. $360^\circ$

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MCQ 71 Mark

The closed curve which is also a polygon is:

Answer

Correct option: A.

is polygon as no two line segments intersect each other.

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MCQ 81 Mark

In the given figure, $\text{ABCD}$ and $\text{BDCE}$ are parallelograms with common base $DC$. If $BC \perp BD$, then $\angle\text{BEC}=$

✓
$60^\circ$
B
$30^\circ$
C
$150^\circ$
D
$120^\circ$

Answer

Correct option: A.

$60^\circ$

$\angle\text{BCD}=30^\circ$
$\therefore\angle\text{BCD}=30^\circ$,
in $\triangle\text{CBD}$ by angle sum property of a triangle, we have
$\Rightarrow\angle\text{DBC}+\angle\text{BCD}+\angle\text{CDB}=180^\circ$
$\Rightarrow90^\circ+30^\circ+\angle\text{CDB}=180^\circ$
$\Rightarrow\angle\text{CDB}=180^\circ-120^\circ=60^\circ$
$\Rightarrow\angle\text{BEC}=60^\circ$

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MCQ 91 Mark

If two adjacent angles of a parallelogram are $(5x – 5)^\circ$ and $(10x + 35)^\circ$, then the ratio of these angles is :

✓
$1 : 3$
B
$2 : 3$
C
$1 : 4$
D
$1 : 2$

Answer

Correct option: A.

$1 : 3$

We know that, adjacent angles of a parallelogram are supplementary,
i.e., their sum equals $180^\circ $
$\therefore (5? − 5) + (10x + 35) = 180^\circ$.
$\Rightarrow 15x+ 30^\circ$.$ = 180^\circ$.
$\Rightarrow 15x = 180^\circ$.
$\Rightarrow x = 10^\circ$.
Thus, the angles are $(5 \times 10 − 5)$ and $(10 \times 10 + 35)$ i.e.,
$45^\circ$ and $135^\circ$.
Hence, the required ratio is $45^\circ : 135^\circ$ i.e., $1:3.$

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MCQ 101 Mark

The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is $30^\circ $. The measure of the obtuse angle is.

A
$100^\circ$
✓
$150^\circ$
C
$105^\circ$
D
$120^\circ$

Answer

Correct option: B.

$150^\circ$

Let $EC$ and $FC$ be altitudes and $\angle\text{EBC}=30^\circ$
let $\angle\text{EDC}=\text{x}=\angle\text{FBC}$
so, $\angle\text{EDC}=90-\text{x}\ \text{and}\ \angle\text{BCF}=90-\text{x}$
So, by property of the parallelogram,
$\Rightarrow\angle\text{ADC}+\angle\text{DCB}+180^\circ$
$\Rightarrow\angle\text{ADC}+(\angle\text{ECD}+\angle\text{ECF})=180^\circ$
$\Rightarrow\text{x}+90^\circ-\text{x}+30^\circ+90^\circ-\text{x}=180^\circ$
$\Rightarrow-\text{x}=180^\circ-210^\circ=-30^\circ$
$\Rightarrow\text{x}=30^\circ$
Hence, $\angle\text{DCB}=30^\circ+60^\circ+60^\circ=150^\circ$

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MCQ 111 Mark

In a parallelogram $\text{PQRS}$, if $\angle\text{P}=60^\circ,$ then other three angles are:

A
$ 45^{\circ}, 135^{\circ}, 120^{\circ} $
✓
$ 60^{\circ}, 120^{\circ}, 120^{\circ} $
C
$ 60^{\circ}, 135^{\circ}, 135^{\circ} $
D
$ 45^{\circ}, 135^{\circ}, 135^{\circ} $

Answer

Correct option: B.

$ 60^{\circ}, 120^{\circ}, 120^{\circ} $

Given,$\angle\text{P}=60^\circ$ Since, in a parallelogram, adjacent angles are supplementary,
$\Rightarrow\angle\text{P}+\angle\text{Q}=180^\circ$
$\Rightarrow60^\circ+\angle\text{Q}=180^\circ$
$\Rightarrow\angle\text{Q}=120^\circ$
Also, opposite angles are equal in a parallelogram
Therefore, $\angle\text{R}=\angle\text{P}=60^\circ,\angle\text{S}=\angle\text{Q}=120^\circ$
Hence, other three angles are $ 60^{\circ}, 120^{\circ}, 120^{\circ} $

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MCQ 121 Mark

Which of the following is not true for an exterior angle of a regular polygon with $n$ sides?

A
Each exterior angle$=\frac{360^\circ}{\text{n}}$
B
Exterior angle $= 180^\circ –$ interior angle
C
$n =\frac{360^\circ}{\text{exterior angle}}$
✓
Each exterior angle $= \frac{(\text{n}-2)\times180^\circ}{\text{n}}$

Answer

Correct option: D.

Each exterior angle $= \frac{(\text{n}-2)\times180^\circ}{\text{n}}$

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MCQ 131 Mark

For which of the following figures, diagonals are equal?

A
Trapezium
B
Rhombus
C
Parallelogram
✓
Rectangle

Answer

Correct option: D.

Rectangle

By the property of a rectangle, we know that its diagonals are equal.

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MCQ 141 Mark

Which of the following is a property of a parallelogram?

✓
Opposite sides are parallel.
B
The diagonals bisect each other at right angles.
C
The diagonals are perpendicular to each other.
D
All angles are equal.

Answer

Correct option: A.

Opposite sides are parallel.

We, know that, in a parallelogram, opposite sides are parallel.

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MCQ 151 Mark

A quadrilateral whose all sides are equal, opposite angles are equal and the diagonals bisect each other at right angles is a __________.

✓
rhombus
B
parallelogram
C
square
D
rectangle

Answer

Correct option: A.

rhombus

We know that, in rhombus, all sides are equal, opposite angles are equal and diagonals bisect each other at right angles.

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MCQ 161 Mark

A quadrilateral whose all sides, diagonals and angles are equal is a.

✓
square
B
trapezium
C
rectangle
D
rhombus

Answer

Correct option: A.

square

These are the properties of a square, i.e. in a square, all sides, diagonals and angles are equal.

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MCQ 171 Mark

Which of the following figures satisfy the following property? - Has two pairs of congruent adjacent sides.

Answer

Correct option: C.

We know that, a kite has two pairs of congruent adjacent sides and we can observe that figure R resembles a kite.

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MCQ 181 Mark

What is the sum of all the angles of a pentagon?

A
$180^\circ$
B
$360^\circ$
✓
$540^\circ$
D
$720^\circ$

Answer

Correct option: C.

$540^\circ$

We know that, the sum of angles of a polygon is $(n - 2) \times 180^\circ $, where n is the number of sides of the polygon.
In pentagon, $n = 5$ Sum of the angles $= (n - 2) \times 180^\circ = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ .$

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MCQ 191 Mark

Which of the following figures satisfy the following properties? All sides are congruent. All angles are right angles. Opposite sides are parallel.

Answer

Correct option: C.

We know that all the properties mentioned above are related to square and we can observe that figure R resembles a square.

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MCQ 201 Mark

Which of the following figures do not satisfy any of the following properties? All sides are equal. All angles are right angles. Opposite sides are parallel.

Answer

Correct option: A.

On observing the above figures, we conclude that the figure P does not satisfy any of the given properties.

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MCQ 211 Mark

The sum of all exterior angles of a triangle is.

A
$180^\circ $
✓
$360^\circ$
C
$540^\circ$
D
$720^\circ$

Answer

Correct option: B.

$360^\circ$

We know that the sum of exterior angles, taken in order of any polygon is $360^\circ $ and triangle is also a polygon. Hence, the sum of all exterior angles of a triangle is $360^\circ .$

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MCQ 221 Mark

What is the maximum number of obtuse angles that a quadrilateral can have?

A
$1$
B
$2$
✓
$3$
D
$4$

Answer

Correct option: C.

$3$

We know that, the sum of all the angles of a quadrilateral is $360^\circ $. Also, an obtuse angle is more than $90^\circ $ and less than $180^\circ .$

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MCQ 231 Mark

In the figure, $\text{BEST}$ is a rhombus, Then the value of $y – x$ is:

✓
$ 40^{\circ} $
B
$ 50^{\circ} $
C
$ 20^{\circ} $
D
$ 10^{\circ} $

Answer

Correct option: A.

$ 40^{\circ} $

Given, a rhombus $\text{BEST} ??\| ??$ and $??$ is transversal.
$\therefore\angle\text{SBE}=\angle\text{TSB}=40^\circ$
Also, $y = 90^\circ$
In $\triangle\text{TSO}, \angle\text{STO}+\angle\text{TOS}=\angle\text{SOE}$
$\Rightarrow \text{x}+40^\circ+90^\circ $
$\Rightarrow\text{x}=50^\circ$
$\Rightarrow\text{y}-\text{x}=90^\circ-50^\circ=40^\circ$

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MCQ 241 Mark

If two adjacent angles of a parallelogram are in the ratio $2 : 3$, then the measure of angles are:

✓
$ 72^{\circ}, 108^{\circ} $
B
$ 36^{\circ}, 54^{\circ} $
C
$ 80^{\circ}, 120^{\circ} $
D
$ 96^{\circ}, 144^{\circ} $

Answer

Correct option: A.

$ 72^{\circ}, 108^{\circ} $

Let the angles be $2x$ and $3x.$ Then, $2 x+3 x=180^{\circ}$
$[$adjacent angles of a parallelogram are supplementary$]$
$\Rightarrow 5 \mathrm{x}=180^{\circ}$
$ \Rightarrow \mathrm{x}=36^{\circ}$
Hence, the measures of angles are $2 \mathrm{x}=2 \times 36^{\circ}=72^{\circ}$ and $3 \mathrm{x}=3 \times 36^{\circ}=108^{\circ}$

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MCQ 251 Mark

A quadrilateral has three acute angles. If each measures $80^\circ $, then the measure of the fourth angle is.

A
$150^\circ $
✓
$120^\circ $
C
$105^\circ$
D
$140^\circ $

Answer

Correct option: B.

$120^\circ $

Let the fourth angle be $x.$
$80^\circ+80^\circ+80^\circ\ \text{x}^\circ=360^\circ$
$\Rightarrow240^\circ+\text{x}=360^\circ$
$\Rightarrow\text{x}=360^\circ-240^\circ$
$\Rightarrow\text{x}=120^\circ$

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MCQ 261 Mark

The angles of a quadrilateral are in the ratio $1 : 2 : 3 : 4$. The smallest angle is.

A
$72^\circ$
B
$144^\circ$
✓
$36^\circ$
D
$18^\circ$

Answer

Correct option: C.

$36^\circ$

Let the angles of the given quadrilaterals be $x^{\circ}, 2 x^{\circ}, 3 x^{\circ}$ and $4 x^{\circ}$
$ \therefore x^{\circ}+2 x^{\circ}+3 x^{\circ}+4 x^{\circ}=360^{\circ} $
$ \Rightarrow 10 x=360^{\circ}$
$ \Rightarrow x=360^{\circ} 10^{\circ}=36^{\circ}$
Hence, the smallest angle $=36^{\circ}$.

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MCQ 271 Mark

Which of the following is an equiangular and equilateral polygon?

✓
Square
B
Rectangle
C
Rhombus
D
Right triangle

Answer

Correct option: A.

Square

In a square, all the sides and all the angles are equal. Hence, square is an equiangular and equilateral polygon.

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MCQ 281 Mark

To construct a unique rectangle, the minimum number of measurements required is:

A
$4$
B
$3$
✓
$2$
D
$1$

Answer

Correct option: C.

$2$

Since, in a rectangle, opposite sides are equal and parallel, so we need the measurement of only two adjacent sides, i.e. length and breadth.

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MCQ 291 Mark

Which of the following figures satisfy the following property? - Only one pair of sides are parallel.

Answer

Correct option: A.

We know that, in a trapezium, only one pair of sides are parallel and we can observe that figure P resembles a trapezium.

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MCQ 301 Mark

Which one has all the properties of a kite and a parallelogram?

A
Trapezium
✓
Rhombus
C
Rectangle
D
Parallelogram

Answer

Correct option: B.

Rhombus

In a kite Two pairs of equal sides. Diagonals bisect at 90°. One pair of opposite angles are equal. In a parallelogram Opposite sides are equal. Opposite angles are equal. Diagonals bisect each other. So, from the given options, all these properties are satisfied by rhombus.

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MCQ 311 Mark

If the diagonals of a quadrilateral are equal and bisect each other, then the quadrilateral is a.

A
rhombus
✓
rectangle
C
square
D
parallelogram

Answer

Correct option: B.

rectangle

Since, diagonals are equal and bisect each other, therefore it will be a rectangle.

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MCQ 321 Mark

The angles $P, Q, R$ and $S$ of a quadrilateral are in the ratio $1:3:7:9.$ Then $PQRS$ is a:

A
parallelogram
✓
trapezium with PQ || RS
C
trapezium with QR||PS
D
kite

Answer

Correct option: B.

trapezium with PQ || RS

Let the angles be $x, 3x, 7x$ and $9x$, then
$\Rightarrow x+3 x+7 x+9 x=360^{\circ} \Rightarrow 20 x=360^{\circ}$
$\Rightarrow x=360^{\circ} 20 \Rightarrow x=18^{\circ}$ Then, the angles $P, Q, R$ and $S$ are $18^{\circ}, 54^{\circ}, 126^{\circ}$ and $162^{\circ}$ respectively Since,
$\angle\text{P}+\angle\text{S}= 18^\circ+162^\circ=180^\circ$ and $\angle\text{Q}+\angle\text{R} = 54^\circ+126^\circ =180^\circ$
The quadrilateral $PQRS$ is a trapezium with $PQ \| RS$

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MCQ 331 Mark

If three angles of a quadrilateral are each equal to $75^\circ ,$ the fourth angle is.

A
$150^{\circ}$
✓
$135^{\circ}$
C
$45^{\circ}$
D
$75^{\circ}$

Answer

Correct option: B.

$135^{\circ}$

Given, three angles of quadrilaterals $=75^{\circ}$
Let the fourth angle be $= x^{\circ}$
Then, according to the property, $75^{\circ}+75^{\circ}+75^{\circ}+x^{\circ}=360^{\circ},$
since sum of the angles of a quadrilateral is $360^{\circ}$.
So, $225^{\circ}+x^{\circ}=360^{\circ}$ or $x^{\circ}=360^{\circ}-225^{\circ}=135^{\circ}$
Hence, the fourth angle is $135^{\circ}$

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MCQ 341 Mark

Which of the following can be four interior angles of a quadrilateral?

✓
$ 140^{\circ}, 40^{\circ}, 20^{\circ}, 160^{\circ} $
B
$ 270^{\circ}, 150^{\circ}, 30^{\circ}, 20^{\circ} $
C
$ 40^{\circ}, 70^{\circ}, 90^{\circ}, 60^{\circ} $
D
$ 110^{\circ}, 40^{\circ}, 30^{\circ}, 180^{\circ} $

Answer

Correct option: A.

$ 140^{\circ}, 40^{\circ}, 20^{\circ}, 160^{\circ} $

We know that, the sum of interior angles of a quadrilateral is $360^\circ$. Thus, the angles in option $(a)$ can be four interior angles of a quadrilateral as their sum is $360^\circ$.

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MCQ 351 Mark

In the trapezium $ABCD$, the measure of $\angle\text{D}$ is.

A
$55^\circ $
B
$115^\circ$
C
$135^\circ$
✓
$125^\circ$

Answer

Correct option: D.

$125^\circ$

We know that, in a trapezium, the angles on either sides of base are supplementary angle. In trapezium $ABCD,$
$\therefore\angle\text{A}+\angle\text{D}=180^\circ$
$\Rightarrow55^\circ+\angle\text{D}=180^\circ$
$\Rightarrow\angle\text{D}=180^\circ-50^\circ$
$\Rightarrow\angle\text{D}=120^\circ$

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MCQ 361 Mark

Which of the following properties describe a trapezium?

✓
A pair of opposite sides is parallel.
B
The diagonals bisect each other.
C
The diagonals are perpendicular to each other.
D
The diagonals are equal.

Answer

Correct option: A.

A pair of opposite sides is parallel.

We know that, in a trapezium, a pair of opposite sides are parallel.

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MCQ 371 Mark

$\text{PQRS}$ is a square. $\text{PR}$ and $\text{SQ}$ intersect at $\text{O}$. Then $\angle\text{POQ}$ is a:

✓
Right angle
B
Straight angle
C
Reflex angle
D
Complete angle

Answer

Correct option: A.

Right angle

We know that, the diagonals of a square intersect each other at right angle. Hence, $\angle\text{POQ}$
$= 90^\circ$
i.e, right angle.

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MCQ 381 Mark

What is the sum of all angles of a hexagon ?

A
$180^{\circ}$
B
$360^{\circ}$
C
$540^{\circ}$
✓
$720^{\circ}$

Answer

Correct option: D.

$720^{\circ}$

Sum of all angles of a $n -$ gon is $(n - 2) \times 180^{\circ}$.
In hexagon, $n = 6$, therefore the required sum $= (6 - 2) \times 180^{\circ}= 4 \times 180^{\circ}= 720^{\circ}$

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MCQ 391 Mark

Which of the following can never be the measure of exterior angle of a regular polygon?

✓
$ 22^{\circ} $
B
$ 36^{\circ} $
C
$ 45^{\circ} $
D
$ 30^{\circ} $

Answer

Correct option: A.

$ 22^{\circ} $

Since, we know that, the sum of measures of exterior angles of a polygon is $ 360^{\circ},$
i.e. measure of each exterior angle $=360^{\circ} n ,$ where n is the number of sides/ angles.
Thus, measure of each exterior angle will always divide $ 360^{\circ} $ completely.
Hence, $22^{\circ} $ can never be the measure of exterior angle of a regular polygon.

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MCQ 401 Mark

For which of the following figures, all angles are equal?

✓
Rectangle
B
Kite
C
Trapezium
D
Rhombus

Answer

Correct option: A.

Rectangle

In a rectangle, all angles are equal, i.e. all equal to $90^\circ .$

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MCQ 411 Mark

To construct a unique parallelogram, the minimum number of measurements required is:

A
$2$
✓
$3$
C
$4$
D
$5$

Answer

Correct option: B.

$3$

We know that, in a parallelogram, opposite sides are equal and parallel. Also, opposite angles are equal. So, to construct a parallelogram uniquely, we require the measure of any two nonparallel sides and the measure of an angle. Hence, the minimum number of measurements required to draw a unique parallelogram is $3.$

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MCQ 421 Mark

If the adjacent sides of a parallelogram are equal then parallelogram is a.

A
rectangle
B
trapezium
✓
rhombus
D
square

Answer

Correct option: C.

rhombus

We know that, in a parallelogram, opposite sides are equal. But according to the question, adjacent sides are also equal. Thus, the parallelogram in which all the sides are equal is known as rhombus.

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MCQ 431 Mark

The number of sides of a regular polygon where each exterior angle has a measure of $45^\circ $ is.

✓
$8$
B
$10$
C
$4$
D
$6$

Answer

Correct option: A.

$8$

We know that, the sum of exterior angles taken in an order of a polygon is $360^\circ $ Since, each exterior angle measures $45^\circ $, therefore the number of sides = Sum of exterior angles/ Measure of an exterior angle.
$=\frac{360^\circ}{45^\circ}=8$

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MCQ 441 Mark

How many diagonals does a hexagon have?

✓
$9$
B
$8$
C
$2$
D
$6$

Answer

Correct option: A.

$9$

We know that, the number of diagonals in a polygon of n sides is $n(n−3) 2$ , In hexagon, $n = 6$ Number of diagonals in a hexagon $= 6(6−3) 2 = 6\times 3 2 = 3 \times 3 = 9.$

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MCQ 451 Mark

Two adjacent angles of a parallelogram are in the ratio $1:5$. Then all the angles of the parallelogram are:

A
$ 30^{\circ}, 150^{\circ}, 30^{\circ}, 150^{\circ} $
B
$ 85^{\circ}, 95^{\circ}, 85^{\circ}, 95^{\circ} $
C
$ 45^{\circ}, 135^{\circ}, 45^{\circ}, 135^{\circ} $
✓
$ 30^{\circ}, 180^{\circ}, 30^{\circ}, 180^{\circ} $

Answer

Correct option: D.

$ 30^{\circ}, 180^{\circ}, 30^{\circ}, 180^{\circ} $

Let the adjacent angles of a parallelogram be $x$ and $5x,$ respectively.
Then, $x + 5x = 180^\circ\ [$adjacent angles of a parallelogram are supplementary$]$
$\Rightarrow 6x = 180^\circ$
$\Rightarrow x = 30^\circ$

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MCQ 461 Mark

For which of the following figures, diagonals are perpendicular to each other?

A
Parallelogram
✓
Kite
C
Trapezium
D
Rectangle

Answer

Correct option: B.

Kite

The diagonals of a kite are perpendicular to each other.

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MCQ 471 Mark

If the adjacent angles of a parallelogram are equal, then the parallelogram is a:

✓
rectangle
B
trapezium
C
rhombus
D
any of the three

Answer

Correct option: A.

rectangle

We know that, the adjacent angles of a parallelogram are supplementary, i.e. their sum equals $180^\circ $ $\&$ given that both the angles are same. Therefore, each angle will be of measure $90^\circ $. Hence, the parallelogram is a rectangle.

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MCQ 481 Mark

For which of the following, diagonals bisect each other?

✓
Square
B
Kite
C
Trapezium
D
Quadrilateral

Answer

Correct option: A.

Square

We know that, the diagonals of a square bisect each other but the diagonals of kite, trapezium and quadrilateral do not bisect each other.

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MCQ 491 Mark

The sum of adjacent angles of a parallelogram is.

✓
$ 180^{\circ} $
B
$ 120^{\circ} $
C
$ 360^{\circ} $
D
$ 90^{\circ} $

Answer

Correct option: A.

$ 180^{\circ} $

By property of the parallelogram, we know that, the sum of adjacent angles of a parallelogram is $180^{\circ} $.

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MCQ 501 Mark

If $\text{PQRS}$ is a parallelogram, then $\angle\text{P}-\angle\text{R}$ is equal to.

A
$ 60^{\circ} $
B
$ 90^{\circ} $
C
$ 80^{\circ} $
✓
$ 0^{\circ} $

Answer

Correct option: D.

$ 0^{\circ} $

Since, in a parallelogram, opposite angles are equal.
Therefore, $\angle\text{P}-\angle{R=0}$ , as, $\angle\text{P} $ and $\angle\text{R}$ are opposite angles.

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MCQ 511 Mark

A parallelogram $\text{PQRS}$ is constructed with sides $QR = 6\ cm, PQ = 4\ cm$ and $\angle \text{PQR} = 90^\circ $. Then $\text{PQRS}$ is a:

A
square
✓
rectangle
C
rhombus
D
trapezium

Answer

Correct option: B.

rectangle

We know that, if in a parallelogram one angle is of $ 90^{\circ} $, then all angles will be of $90^{\circ} $ and a parallelogram with all angles equal to $ 90^{\circ} $ is called a rectangle.

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