In fig. ABCD is a parallelogram. What are the values of $$p$$ and $$q$$ ? If $$\angle CBE$$ = $$100^{\circ}$$.

$$\angle p = 80^o, \angle q = 100^o$$

$$\angle p = 100^o, \angle q = 80^o$$

MCQ Questions for Class 8 Maths Understanding Quadrilaterals Quiz 8

Two adjacent angles of a parallelogram are

$2x+ 30^o$ and

$5x + 30^o$ . Then the value of

$x$ is ___ .

0%
$\dfrac{180^o}{7}$
0%
$\dfrac{120^o}{7}$
0%
$\dfrac{60^o}{7}$
0%
None of these.

Explanation

Sum of two adjacent angles in a parallelogram is

$180^o$ .

$\therefore \ 2x + 30^o + 5x + 30^o = 180^o$

$\Rightarrow 7x+60^o=180^o$

$\Rightarrow 7x = 120^o$

$\Rightarrow x = \dfrac{120^o}{7}$

Two consecutive angles of a parallelogram are in ratio

$1 : 6$ , then the smaller angle is:

0%
$\dfrac{1080}{7}$
0%
$\dfrac{180}{7}$
0%
$\dfrac{540}{7}$
0%
None

Explanation

${\textbf{Step - 1: Drawing a figure of parallelogram and marking the angles}}$

${\text{Let the smaller angle be x}}$

${\text{Since the angle are in the ratio 1 : 6, the larger angle will be 6x}}$

${\textbf{Step - 2: Finding the angles}}$

${\text{We know that, two adjacent angles of a parallelogram are supplementary,}}$

$\Rightarrow {\text{ x + 6x = 180}}^\circ$

$\Rightarrow {\text{ 7x = 180}}^\circ$

$\Rightarrow {\text{ x = }}\dfrac{{{\text{180}}}}{{\text{7}}}^\circ$

$\therefore {\text{ x = }}\dfrac{{{\text{108}}}}{{\text{7}}}^\circ$

$\mathbf{{\text{Hence, The measure of smaller angle is (B) }}\dfrac{{{\text{180}}}}{{\text{7}}}^\circ }$

In fig. ABCD is a parallelogram. What are the values of

$p$ and

$q$ ?

$\angle CBE$ =

$100^{\circ}$ .

0%
$\angle p = 100^o, \angle q = 80^o$
0%
$\angle p = 80^o, \angle q = 100^o$
0%
$\angle p = \angle q$
0%
None

Explanation

$\angle CBE = 100, \angle p + \angle CBE = 180^o, \angle p = 180 - 100, \angle p = 80^o$

$\angle q = \angle CBE, [\because AD || BC]$

$\therefore \angle q = 100^o$

Identify the Quadrilateral.

0%
parallelogram
0%
rectangle
0%
square
0%
trapezium

In parallelogram, both pairs of opposite sides are ....................

0%
equal
0%
parallel and equal
0%
perpendicular
0%
perpendicular and equal

Explanation

$ABCD$ is a parallelogram,

$\Rightarrow$ We know that

$AB\parallel CD$

Here

$AC$ is a transversal for the parallel lines

$AB$ and

$CD$

$\Rightarrow$ So,

$\angle BAC = \angle DCA$ [Alternate interior angles are equal]

$... ( 1 )$

$\Rightarrow$ Similarly, we know that

$BC\parallel AD$

$\Rightarrow \angle BCA = \angle DAC$

$... ( 2 )$

$\triangle ABC$ and

$\triangle ADC,$

We have

$\angle BAC = \angle DCA$ [From ( 1 )]

$\Rightarrow$

$AC$ is the common side

$\Rightarrow \angle BCA = \angle DAC$ [From ( 2 )]

$\Rightarrow$ So,

$\triangle ABC \cong \triangle CDA$ [As per ASA Congruence rule]

$\therefore AB = CD$ and

$BC = AD$ [Corresponding sides of congruent triangle are equal ]

Hence, both pairs of opposite sides in a parallelogram are parallel and equal.

PQRS is a parallelogram & PA & RB are perpendicular from P & R in diagonal SQ. Which of following is the correct option?

0%
$AP = BQ$
0%
$PA = BR$
0%
$AS = RB$
0%
None

Explanation

$\triangle APQ$ &

$\triangle RSB$ ,

$\angle PAQ = \angle SBR$ ......each

$90^o$

$PQ = SR$ ......(opposite sides of parallelogram)

$\angle AQP = \angle RSB$ .....(Alternate angle)

$\therefore \triangle APQ \cong \triangle RSB$

$\therefore PA = BR$ .....cpct

In the given parallelogram, find the opposite angle

$y$ ?

0%
$60^o$
0%
$50^o$
0%
$70^o$
0%
$120^o$

Explanation

$y=120^o$ (as opposite angles in a parallelogram are equal)
Therefore, D is the correct answer.

The diagonals AC & BD of parallelogram ABCD intersect each other at P of

$\angle DAC = 40^o$ &

$\angle APB = 80^o$ . Then

$\angle DBC$ is equal to ___ .

0%
$40^o$
0%
$80^o$
0%
$120^o$
0%
None

Explanation

ABCD in parallelogram

$AD || BC \therefore \angle D AC = \angle BCA$

$\angle APB = \angle ACB + \angle DBC$ (Exterior angle of a triangle)

$\angle DBC = \angle APB - \angle ACB$

$\angle DBC = 80^o - \angle DAC$

$\angle DBC = 80^o - 40^o$

$\angle DBC = 40^o$

$WXYZ$ is a parallelogram & its diagonals intersect at point

$O$ . Find

$\angle OZY$ .

0%
$115^o$
0%
$65^o$
0%
$60^o$
0%
$70^o$

Explanation

In parallelogram

$WXYZ,$

$\angle ZWX = 30^o + 35^o = 65^o$

We know opposite angles of a parallelogram are equal

Hence

$\angle ZWX = \angle XYZ = 65^o$

We know the sum of any two adjacent angles of a parallelogram is

$180^\circ$

$\Rightarrow\angle Z = 180^o - \angle W$

$= 180^o - 65^o$

$= 115^o$

$\triangle WOX,$

$\Rightarrow \angle OXW + \angle WXO + \angle WOX = 180^o$

$\Rightarrow \angle WXO = 180^o - 30^o - 80^o$

$\Rightarrow \angle WXO = 70^o$

$\therefore \angle XZY = \angle OZY = 70^o\ \ \ \ \ \ \ (\because WX \parallel ZY)$

PQRS is a parallelogram and side RS is smaller than side QR. Then the relation between

$\angle 1$ and

$\angle 2$ is ___ .

0%
$\angle 1 < \angle 2$
0%
$\angle 1 > \angle 2$
0%
$\angle 1 = \angle 2$
0%
None

Explanation

$\angle 1 = \angle RSQ$ ....alternate angles

$\triangle RSQ$ ,

$RS<QR$ ...given

$\therefore \angle 2 < \angle RSQ$ ....angle opp to shorter side is smaller

i.e.

$\therefore \angle 2 < \angle 1$

PQRS is a parallelogram, the bisector of

$\angle$ P also bisects SQ, PQ = 5 cm. Find PS.

0%
5 cm
0%
7 cm
0%
10 cm
0%
Cant determine

If ABCD is a parallelogram, then how are the angles 'x' and 'y' related?

0%
x = y
0%
x > y
0%
x < y
0%
Can't be determined

The value of

$xy$ for parallelogram

$ABCD$ is :

0%
$2,695$
0%
$2,940$
0%
$4,704$
0%
$6,468$

Explanation

Opposite angles in a parallelogram are equal, implying

$\angle ADC = \angle ABC$

$\therefore x + y = 112 ...(1)$

Also,

$\angle DAC = \angle BCA$ since they are alternate angles.

$\therefore x - y = 42 ...(2)$

Adding equations (1) and (2), we get

$2x = 154$ or

$x = 77$

$\Rightarrow y = 77 - 42 = 35$

Therefore,

$xy = 77 \times 35 = 2695$

In a parallelogram

$ABCD$ ,

$AB=4\ cm$ and

$BC = 7\ cm$ . Each of its diagonals is less than which of the given options?

0%
$3\ cm$
0%
$6\ cm$
0%
$7\ cm$
0%
$11\ cm$

Explanation

For a parallelogram ABCD,

$diagonal\quad AC>AB+BC\\ AC>7+4\\ AC>11cm$

So, option D is correct.

The perimeter of a parallelogram,whose one side measures

$12$ inches, is 72 inches. Find the length of its other three sides.

0%
$12, 12, 36$
0%
$12, 18, 18$
0%
$12, 24, 24$
0%
$12, 30, 30$

In figure, if

$ABCD$ is a parallelogram,

$\angle ADE = 40^{\circ}$ , and

$\angle C = 110^{\circ}$ , calculate the measure of

$\angle BED$ .

0%
$30^{\circ}$
0%
$40^{\circ}$
0%
$70^{\circ}$
0%
$110^{\circ}$
0%
$150^{\circ}$

Explanation

Given,

$\angle$

$C$

$=$

$110^o, \angle ADE = 40^o$

$\angle$

$D=\angle B$ {Opposite angle}

Also,

$\angle D + \angle C = 180^o$ {because these interior angles lie on the same side of the transversal}

$\angle D=180^o-110^o = 70^o$

Therefore,

$\angle$

$EDC =\angle D- \angle ADE = 70^o-40^o = 30^o$

$\angle$

$EBC = \angle B = 70^o$ ,

$\angle$

$DCB = 110^o$

Therefore,

$\angle$

$BED = 360^o-110^o-70^o-30^o = 150^o$ {Sum of angle of quadrilateral EBCD =

$360^o$ }

In the given figure, find

$\angle BDC$ .

0%
${ 60 }^{ o }$
0%
${ 75 }^{ o }$
0%
${ 45 }^{ o }$
0%
${ 50 }^{ o }$

Explanation

Let given quadrilateral

$ABCD$ is a parallelogram.

Then,

$AB$ is parallel to

$CD$ and

$AD$ is parallel to

$BC$ (Opposite sides of parallelogram are parallel)

$\Rightarrow \angle$ DAB

$=$

$\angle$ BCD (Opposite angles of parallelogram are equal)

Since, it is given that

$\angle$ DAB

$=$ 75

$^\circ$ .

Then,

$\angle$ BCD

$=$ 75

$^\circ$ ---- (1)

$\Rightarrow$

$\angle$ DBC = 60

$^\circ$ ---- (2) (Given)

$\triangle$ DCB,

$\angle$ BDC +

$\angle$ BCD +

$\angle$ DBC

$= 180$

$^\circ$

$\angle$ BDC + 75

$^\circ$ + 60

$^\circ$

$=$ 180

$^\circ$ [From (1) and (2) ]

$\angle$ BDC

$=$ 180

$^\circ$ - 135

$^\circ$

$\therefore$

$\angle BDC = 45^\circ$

The diagonals of a parallelogram

$ABCD$ intersect at

$O$ . A line through O intersect AB at X and DC at Y. Identify the correct option

0%
$OX = OY$
0%
$OX > OY$
0%
$OX < OY$
0%
$OX - OY = 0$

Explanation

$\Rightarrow$ In given figure ABCD is a parallelogram.

$\therefore$ AB

$\parallel$ DC

$\Rightarrow$ Also AC is a transversal of AB

$\parallel$ DC.

$\therefore$

$\angle1=\angle2$ [Alternate interior angles]

$\Rightarrow$ Now in

$\triangle$ AXO and

$\triangle$ CYO, we have

$\Rightarrow$

$\angle1=\angle2$ [Alternate interior angles]

$\Rightarrow$

$\angle3=\angle4$ [Vertically opposite angles]

$\Rightarrow$

$CO=OA$ [Diagonals bisect each other]

$\therefore$

$\triangle AXO \cong \triangle CYO$ [ASA Criteria]

$\therefore$

$OX=OY$ [CPCT]

The interior angles of a pentagon are in the ratio 2:3:4:5:6 respectively. Then sum of the first and second angle is

0%
$90 ^ { \circ }$
0%
$140 ^ { \circ }$
0%
$135 ^ { \circ }$
0%
$180 ^ { \circ }$

What do you call a parallelogram which has equal diagonals?

0%
A trapezium
0%
A rectangle
0%
A rhombus
0%
A kite

Explanation

$\Rightarrow$ A parallelogram which has equal diagonals are called rectangle.

$\Rightarrow$ Trapezium, rhombus and kite does not contain equal diagonal.

$\Rightarrow$ Proof for rectangle contains equal diagonals are given below :-

$\Rightarrow$ In given figure ABCD is a rectangle.

$\Rightarrow$ In

$\triangle$ ABC and

$\triangle$ DCB

$\Rightarrow$ BC = CB [Common]

$\Rightarrow$ AB = DC [Opposite sides of rectangle]

$\Rightarrow$

$\angle$ ABC =

$\angle$ DCA = 90

$^\circ$ [Each angle of rectangle is 90

$^\circ$ ]

$\Rightarrow$

$\triangle$ ABC

$\cong$

$\triangle$ DCB [By SAS property]

$\therefore$ AC = BD [By CPCT]

ABCD is a parallelogram in which

$\angle A = (x+20)^\circ$ and

$\angle C = (3x -10)^\circ$ . Find the value of

$x$ .

0%
$60^\circ$
0%
$40^\circ$
0%
$30^\circ$
0%
$15^\circ$

Explanation

In given figure ABCD is a parallelogram.

We have given that,

$\angle A =(x+20)^\circ$ and

$\angle C = (3x-10)^\circ$

We know that opposite angles of parallelogram are equal.

So,

$\angle A = \angle C$

$(x+20)^\circ=(3x-10)^\circ$

$2x^\circ =30^\circ$

$\therefore$

$x = 15^\circ$

$ABCD$ is a parallelogram and

$X, Y$ are the mid-points of sides

$AB$ and

$CD$ respectively. What is the quadrilateral

$AXCY$ ?

0%
Parallelogram
0%
Rhombus
0%
Square
0%
Rectangle

Find the measure of each angle of a parallelogram, if largest angle is

$\displaystyle { 30 }^{ \circ }$ less than twice the smallest angle.

0%
$\displaystyle { 60 }^{ \circ },{ 100 }^{ \circ },{ 90 }^{ \circ },{ 20 }^{ \circ }$
0%
$\displaystyle { 80 }^{ \circ },{ 40 }^{ \circ },{ 120 }^{ \circ },{ 90 }^{ \circ }$
0%
$\displaystyle { 100 }^{ \circ },{ 90 }^{ \circ },{ 90 }^{ \circ },{ 80 }^{ \circ }$
0%
$\displaystyle { 70 }^{ \circ },{ 110 }^{ \circ },{ 70 }^{ \circ },{ 110 }^{ \circ }$

Explanation

Sum of angles of parallelogram is

$360^o$

$\Rightarrow x+(2x-30)+x+(2x-30)=360^o$

$x^o+(2x-30)^o+x^o +(2x-30)^o=360^o$

$6x^o=420^o$

$\Rightarrow {x^o=70^o}$

$(2x-30)^o=2\times70^o$

$-30^o$

$=110^o$

$\Rightarrow\boxed {angles \,are 70^o,110^o,70^o,110}$

The figure below is a parallelogram with two angles given in terms of x. Determine the value of x.

0%
$9$
0%
$10$
0%
$20$
0%
$22$
0%
$24$

Explanation

We know that, adjacent angles of a parallelogram are supplementary; that is, they add to

$180^o$ .

Use this to set up an equation, and then solve it for

$x$ .

$\therefore \ (4x + 12) + (3x + 14)=180$

$\Rightarrow 7x +26 =180$

$\Rightarrow 7x=154$

$\Rightarrow x=22$

Hence, the value of

$x$ is

$22$ .

The diagonals of a parallelogram divide the figure into four triangles that are

0%
congruent
0%
similar
0%
equal in area
0%
isosceles
0%
none of these

Identify the true statement with respect to the given figure

0%
$ar (POQ) + ar(SOR) = ar(POS) + ar(QOR)$
0%
$ar(POQ + ar(POS) = ar(ROQ) + ar(ROS)$
0%
Both the true (A) and (B)
0%
Neither (A) nor (B) is true

Diagonal of a parallelogram separates it into

0%
Two triangles of equal area
0%
Two congruent triangles
0%
Both a and b
0%
None

Explanation

$\Delta ABC$ &

$\Delta ADC$

$BC=AD$

$DC=AB$

$\angle CBA=\angle ADC=\theta$

$\therefore$ By SAS rule

$\Delta ABC$ is congruent to

$\Delta ADC$

$\therefore$ also have equal area.

1065023_509680_ans_4945bf4cf6b64942850d6d9ae2899d01.png

In the parallelogram, what is the value of "x"?

0%
$30$
0%
$50$
0%
$70$
0%
$80$

Explanation

By using properties of

$119m$

$\theta =80^{\circ}$

Using exterior angle property

$\theta +x=150^{\circ}$

$\Rightarrow \boxed{x=70^{\circ}}$

1064920_509669_ans_670bba06ec3a4320a3a937a0b4a87603.png

Tick these figures which are simple closed curves.

All squares are not parallelograms.

0%
True
0%
False

Explanation

$\Rightarrow$ A parallelogram is a quadrilateral with opposite sides parallel and sum of its adjacent sides are supplementary.

$\Rightarrow$ In square opposite sides are parallel and measure of each angle is

$90^o$ , so sum of its adjacent also supplementary.

$\Rightarrow$ So, square contains all the properties of a parallelogram.

$\therefore$ All squares are parallelogram.

So, given statement is false.

CBSE Questions for Class 8 Maths Understanding Quadrilaterals Quiz 8 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

CBSE Questions for Class 8 Maths Understanding Quadrilaterals Quiz 8 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

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