MCQ Questions for Class 9 Maths Lines And Angles Quiz 8

From the adjacent figure find the values of

$\angle P R S$ (in degree).

0%
$85$
0%
$75$
0%
$65$
0%
$55$

Explanation

We know, by exterior angle property, an exterior angle of a triangle is equal to the sum of the two interior opposite angles.

Then, in

$\triangle PQR$ ,

$\angle QPR+\angle PQR = \angle PRS$

$\implies$

$35^{o}+50^{o} = \angle PRS$

$\implies$

$\angle PRS = 85^{o}$ .

Therefore, option

$A$ is correct.

In the given figure

$\angle P Q R = \angle P R Q$ .

in this question the statement is

$\angle P Q S \ne \angle P R T$ .

0%
True
0%
False

Explanation

Let

$\angle PQR=\angle PRQ=x$ (say).....(1)

Now,

$\angle PQS+\angle PQR=180^o$ [Linear pair of angles]

and

$\angle PRT+\angle PRQ=180^o$ [Linear pair of angles]

$\Rightarrow \angle PQS+\angle PQR=\angle PRT+\angle PRQ [\because each=180^o]$

$\Rightarrow \angle PQS+x=\angle PRT+x$ [By (1)]

$\Rightarrow \angle PQS=\angle PRT$ .

Hence, the statement is false and option

$B$ is correct.

Find the complement of the angle

$63^o$

0%
${70^ \circ}$
0%
${27^ \circ}$
0%
${45^ \circ}$
0%
${62^ \circ}32'$

Explanation

We know, two angles are complementary when they add up to $90^o.$

Given, measure of one complementary angle is $63^o.$

$\Rightarrow$ Measure of other complementary angle $=90^o-63^o$ $=27^o.$

$\therefore$ Measure of a complementary angle of $63^{o}=27^o$ .

Hence, option $B$ is correct.

The measure of an acute angle is always

$< 90^{o}$ .

0%
True
0%
False

Explanation

Acute angles are the angles whose measurements fall between

$0$ and

$90$ degrees.

$\therefore$ The above statement is true.

Which of the following pairs represents pairof corresponding angles.

0%
$\angle a$ and $\angle d$
0%
$\angle a$ and $\angle e$
0%
$\angle \mathrm { d }$ and $\angle i$
0%
$\angle \mathrm { c }$ and $\angle \mathrm { h }$

In triangle, three angles are

$x , x + 10 ^ { \circ } + x + 20 ^ { \circ }$ then the biggest is

0%
$70 ^ { \circ }$
0%
$80 ^ { \circ }$
0%
$90 ^ { \circ }$
0%
none

Find the lettered angle :

0%
$110^{\circ}$
0%
$70^{\circ}$
0%
$30^{\circ}$
0%
$90^{\circ}$

If the angles of triangle are in the ratio

$1:4:7$ , then the value of the largest angle is :

0%
$135^{\circ}$
0%
$84^{\circ}$
0%
$105^{\circ}$
0%
none of these

If the supplement of an angle is

$\dfrac { 5 }{ 2 }$ times the complement of the same angle, find the supplementary angle.

0%
${ 150 }^{ \circ }$
0%
${ 60 }^{ \circ }$
0%
${ 30 }^{ \circ }$
0%
${ 120 }^{ \circ }$

The complementary angle of

$75^{\circ}$ is _______.

0%
$75^{\circ}$
0%
$105^{\circ}$
0%
$15^{\circ}$
0%
$25^{\circ}$

Explanation

We know, two angles are complementary when they add up to $90^o.$

Given, measure of one complementary angle is $75^o.$

$\Rightarrow$ Measure of other complementary angle $=90^o-75^o$ $=15^o.$

$\therefore$ Measure of a complementary angle of $75^{o}=15^o$ .

Hence, option $C$ is correct.

In the figure below,

$AA'$ is parallel to

$CC'$ . The measure

$w$ of

$\angle A'AB$ is equal to

$135^\circ$ and the measure

$z$ of

$\angle C'CB$ is equal to

$147^\circ$ . Find

$\angle ABC$ .

0%
$100^\circ$
0%
$78^\circ$
0%
$80^\circ$
0%
$110^\circ$

Explanation

Draw

$BB'$ parallel to

$AA'$ and

$CC'$ as shown in the figure below.

Note that angle

$ABC$ is given by

$\angle ABC = \angle ABB' + \angle CBB'$

$\angle w'$ and

$\angle ABB'$ are alternate interior angles and their measure are equal.

$\angle ABB' = \angle w'$

$\angle z'$ and

$\angle CBB'$ are alternate interior angles and their sizes are equal.

$\angle CBB' = \angle z'$

Angles

$w$ and

$w'$ are supplementary which gives

$w' = 180^\circ - w$

$= 180^\circ - 135^\circ$

$= 45^\circ$

Angles

$z$ and

$z'$ are also supplementary which gives

$z' = 180^\circ - z$

$= 180^\circ - 147^\circ$

$= 33^\circ$

We now substitute

$\angle ABB'$ by

$w'$ and

$\angle CBB'$ by

$z'$ in

$\angle ABC = \angle ABB' + \angle CBB'$ found above.

$\angle ABC = w' + z'$

$= 45^\circ + 33^\circ$

$= 78^\circ$

1372052_1612546_ans_cd420c00d05f4cecb59ce0d2f619972f.PNG

Complement of

$60^o$ is?

0%
$30^o$
0%
$130^o$
0%
$120^o$
0%
$90^o$

Explanation

We know, two angles are complementary when they add up to $90^o.$

Given, measure of one complementary angle is $60^o.$

$\Rightarrow$ Measure of other complementary angle $=90^o-60^o$ $=30^o.$

$\therefore$ Measure of a complementary angle of $60^{o}=30^o$ .

Hence, option $A$ is correct.

Which of the following statements are true (T) and which are false (F)?
Angles forming a linear pair are supplementary.

0%
True
0%
False

Mark the correct alternative of the following.
An angle of measure

$140^o$ is?

0%
An acute angle
0%
An obtuse angle
0%
A straight angle
0%
A complete angle

Explanation

An angle that measures

$<180^o$ but

$>90^o$ is called an obtuse angle.

Here it is given

$140^o$ , so it is an obtuse angle.

Mark the correct alternative of the following.
The sum of an angle and one third of its supplementary angle is

$90^o$ . The measure of the angle is?

0%
$135^o$
0%
$120^o$
0%
$60^o$
0%
$45^o$

Explanation

Let, required angle be

$x$ and its supplementary angle be

$(180-x)$ .

$\therefore \angle x+\angle (180-x)=180^0$

According to condition, the sum of an angle and one third of its supplementary angle is

$90^0$

$\angle x+\dfrac{1}3\angle (180-x)=90^0\\$

$\angle x+\dfrac{1}3(180^0-x)=90^0\\$

$\dfrac2{3}\angle x+60^0=90^0\\$

$\dfrac2{3}\angle x=30^0\\$

$\angle x=45^0\\$

$\therefore$ measure of a required angle is

$45^0$

Mark the correct alternative of the following.
In figure, if AB

$||$ CD then the value of x is?

0%
$34$
0%
$124$
0%
$24$
0%
$158$

Two supplementary angles are in the ratio

$3:2$ . The smaller angle measures?

0%
$108^o$
0%
$81^o$
0%
$72^o$
0%
$68^o$

Explanation

Given two supplementary angles are in the ratio

$3:2$ .

Let the measurement of the angles be

$3x$ and

$2x$ .

Two angles are said to be supplementary if they sum upto

$180^o$ .

Then we have,

$3x+2x=180^{o}$

$5x=180^o$

or,

$x=36^o$ .

So the smaller angle is

$36^o\times 2=72^o$ .

The complement of

$80^{o}$ is:

0%
$100^{o}$
0%
$10^{o}$
0%
$20^{o}$
0%
$280^{o}$

Explanation

Two angles are said to be complementary, if the sum of their measures is

$90^{o}$ .

The given angle is

$80^{o}$ .

Let the measure of its supplement be

$x^{o}$ .

Then,

$\implies x^{o}+80^{o}=90^{o}$

$\implies x=90^o-80^o$

$\implies x=10^o$ .

Hence, the supplement of the given angle measures

$10^{o}$ .

Therefore, option

$B$ is correct.

Mark the correct alternative of the following:
In figure,

$AB||CD||EF$ ,

$\angle ABG=110^o$ ,

$\angle GCD=100^o$ and

$\angle BGC=x^o$ . The value of

$x$ is?

0%
$35$
0%
$50$
0%
$30$
0%
$40$

Explanation

In figure

$AB\ ||\ CD\ ||\ EF$ ,

$\angle ABG=110^0, \angle GCD=100^0$ .

Also,

$\angle ABG$ and

$\angle BGE$ ,

$\angle GCD$ and

$\angle CGF$ are pair of interior angles on same side of the transversal are supplementary.

$\therefore \angle ABG+\angle BGE=180^0$

$\therefore 110^0+\angle BGE=180^0$

$\therefore \angle BGE=70^0$ .

Similarly,

$\therefore \angle GCD+\angle CGF=180^0$

$\therefore 100^0+\angle CGF=180^0$

$\therefore \angle CGF=80^0$ .

Now,

$\angle BGE+\angle BGC+\angle CGF=180^0$ ...{sum of angles on one side of a straight line is

$180^o$ }

$\therefore 70^0+x+80^0=180^0$

$\therefore x+150^0=180^0$

$\therefore x=30^0$ .

Hence, option

$C$ is correct.

Mark the correct alternative of the following:
The sum of an angle and half of its complementary angle is

$75^o$ . The measure of the angle is?

0%
$40^o$
0%
$50^o$
0%
$60^o$
0%
$80^o$

Explanation

Given, the sum of angle and half its complementary angle is

$75^o$ .

We know, sum of the complementary angles is

$90^{ \circ }$ .

Then, let the angles be

$x$ and

$(90^o-x)$ .

Now,

$x+\dfrac{1}{2}(90^o-x)={ 75 }^{ \circ }$

$\implies$

$x-\dfrac{1}{2}x+45^o={ 75 }^{ \circ }$

$\implies$

$\dfrac{1}{2}x={ 75 }^{ o }-45^o$

$\implies$

$\dfrac{1}{2}x=30^o$

$\implies$

$x= 2\times30^o=60^o$ .

Hence, the measure of the required angle is

$60^o$ .

Therefore, option

$C$ is correct.

Mark the correct alternative of the following.
In figure, if AC

$||$ DF and AB

$||$ CE, then?

0%
$x=145$ , $y=223$
0%
$x=223$ , $y=145$
0%
$x=135$ , $y=233$
0%
$x=233$ , $y=135$

Mark the correct alternative of the following.
In figure, if AB

$||$ CD then

$x=?$

0%
$54$
0%
$39$
0%
$44$
0%
$64$

Mark the correct alternative of the following:
Two complementary angles are in the ratio

$2:3$ . The measure of the larger angle is?

0%
$60^o$
0%
$54^o$
0%
$66^o$
0%
$48^o$

Explanation

Given, the complementary angles are in the ratio

$2:3$ .

Let the angles be

$2x$ and

$3x$ .

We know, sum of the complementary angles is

$90^{ \circ }$ .

$\Rightarrow 2x+3x={ 90 }^{ \circ }\\ \Rightarrow 5x=9{ 0 }^{ \circ }\\ \Rightarrow x=18^{ \circ }$

Hence, the angles are:

$2x=2\times 18^{ \circ }=36^{ \circ }$

and

$3x=3\times 18^{ \circ }=54^{ \circ }$ .

Here, the larger angle is

$54^o$ .

Therefore, option

$B$ is correct.

Mark the correct alternative of the following.

$\angle A$ is an obtuse angle. The measure of

$\angle A$ and twice its supplementary differ by

$30^o$ . Then,

$\angle A$ can be?

0%
$130^o$
0%
$110^o$
0%
$140^o$
0%
$120^o$

Explanation

Given,

$\angle A$ is an obtuse angle.

Let, its supplementary angle be

$B$ .

$\therefore \angle A+\angle B=180^0$

$\therefore \angle A=180^0-\angle B$ ...

$(1)$

According to condition, the measure of

$\angle A$ and twice its supplementary differ by

$30^0$ .

So, we have

$2$ cases:

Case

$1:$

$\therefore \angle A-2\angle B=30^0$

$\implies$

$180^0-\angle B-2\angle B=30^0$ .. From

$(1)$

$\implies$

$180^0-3\angle B=30^0$

$\implies$

$3\angle B=150^0$

$\implies$

$\angle B=50^0$

$\implies$

$\angle A=130^0$ .

Case

$2:$

$\therefore 2\angle B-\angle A=30^0$

$\implies$

$2\angle B-180^0+\angle B=30^0$ .. From

$(1)$

$\implies$

$3\angle B=210^0$

$\implies$

$\angle B=70^0$

$\implies$

$\angle A=110^0$ .

$\therefore \angle A$ can be

$110^0$ or

$130^0$ .

Hence, option

$A$ and

$B$ are correct.

An angle is its own complement. The measure of the angle is:

0%
$30^{o}$
0%
$45^{o}$
0%
$90^{o}$
0%
$60^{o}$

Explanation

Let the measure of the required angle be

$x^{o}$ .

Since, the angle is its own complement, both the angle and its complement will be equal.

Then,

$\implies x^{o}+x^{o}=90^{o}$

$\implies 2x=90^o$

$\implies x=\dfrac{90}{2}^o$

$\implies x=45^o$ .

Hence, the required angle measures

$45^{o}$ .

Therefore, option

$B$ is correct.

An angle is

$24^{o}$ more than its complement. The measure of the angle is:

0%
$47^{o}$
0%
$57^{o}$
0%
$53^{o}$
0%
$66^{o}$

Explanation

Let the measure of the angle be

$x^o$ .

Let the measure of its complement be

$(x-24^{o})$ .

Then,

$x^{o} + (x-24)^{o}$ =

$90^{o}$

$\implies$

$x+x=90^o+24$

$\implies$

$2x=114$

$\implies$

$x=57$

$\implies$

$x=57^o$ .

Therefore, option

$B$ is correct.

The supplement of

$45^{o}$ is

0%
$45^{o}$
0%
$75^{o}$
0%
$135^{o}$
0%
$155^{o}$

Explanation

Two angles are said to be supplementary if the sum of their measures is

$180^{o}$ .

The given angle is

$45^{o}$

Let the measure of its supplement be

$X^{o}$ .

Then,

$\implies X+45=180$

$\implies X=180-45$

$\implies X=135$

Hence, the supplement of the given angle measures

$135^{o}$ .

An angle measuring

$270^{o}$ is:

0%
an obtuse angle
0%
an acute angle
0%
a straight angle
0%
a reflex angle

Explanation

The given measure of angle is

$270^o.$

Reflex angles are angles measuring greater than

$180^o$ and less than

$360^o.$

$\therefore$

$270^o$ is a reflex angle.

Hence, option

$D$ is correct.

In the adjoining figure, what value of

$x$ will make

$AOB$ a straight line?

0%
$x$ = $30$
0%
$x$ = $35$
0%
$x$ = $25$
0%
$x$ = $40$

Explanation

(b)

$x$ =

$35$
Because,
It is given that the angles of the side be

$(2x-10)^{o}$ and

$(3x+15)^{o}$ .
=

$(2x-10) + (3x+15)$ =

$180$ ...

$[\because Linear\,pair]$
=

$2x-10+3x + 15$ =

$180$
=

$5x + 5$ =

$180$
=

$5x$ =

$180-5$
=

$x$ =

$175/5$
=

$x$ =

$35$

In the given figure, what value of

$x$ will make

$AOB$ a straight line?

0%
$x$ = $50$
0%
$x$ = $100$
0%
$x$ = $60$
0%
$x$ = $80$

Explanation

(d)

$x$ =

$80$
Because,
It is given that the angles of the side be

$55^{o}$ ,

$45^{o}$ and

$(x)^{o}$ .
=

$x^{o} + 55^{o} + 45^{o}$ =

$180^{o}$ ...

$[\because Linear\,pair]$
=

$x$ =

$180-100$
=

$x$ =

$80$

CBSE Questions for Class 9 Maths Lines And Angles Quiz 8 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Lines And Angles Quiz 8 - MCQExams.com

0:0:1

Practice Class 9 Maths Quiz Questions and Answers

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