MCQ Questions for Class 9 Maths Lines And Angles Quiz 3

Choose the pair of complementary angles:

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$30^{\circ}$ , $150^{\circ}$
0%
$76^{\circ}$ , $14^{\circ}$
0%
$65^{\circ}$ , $65^{\circ}$
0%
$120^{\circ}$ , $30^{\circ}$

Explanation

We know, two angles whose sum is equal to $90^o$ are known as complementary angles.

Consider option $(A)$ .

The angles are $30^o$ and $150^o$ .

Then their sum $=30^o+150^o=180^o\ne90^o$ .

Hence, the angles are not complementary.

Consider option $(B)$ .

The angles are $76^o$ and $14^o$ .

Then their sum $=76^o+14^o=90^o$ .

Hence, the angles are complementary.

Consider option $(C)$ .

The angles are $65^o$ and $65^o$ .

Then their sum $=65^o+65^o=130^o\ne90^o$ .

Hence, the angles are not complementary.

Consider option $(D)$ .

The angles are $120^o$ and $30^o$ .

Then their sum $=120^o+30^o=150^o\ne90^o$ .

Hence, the angles are not complementary.

Hence, only option $B$ is correct.

Supplementary angle of

$100^{\circ}$ is

0%
$180^{\circ}$
0%
$90^{\circ}$
0%
$80^{\circ}$
0%
$60^{\circ}$

Explanation

Let the supplement be

$x$

If angles are supplementary then their sum is

$180^{\circ}$

$\Rightarrow x+100^{\circ}=180^{\circ}$

$x=180^{\circ}-100^{\circ}$

$x=80^{\circ}$

Measure of an obtuse angle is:

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$> 0^{\circ}, < 90^{\circ}$
0%
$> 90^{\circ}, < 180^{\circ}$
0%
$> 0^{\circ}, < 270^{\circ}$
0%
$> 0^{\circ}, < 180^{\circ}$

Explanation

Measure of an obtuse angle is always greater than

$0^o$ and less than

$180^o$ .

Therefore, it can be written as

Obtuse angle is

$>$

$90^{\circ}$ &

$<$

$180^{\circ}$

Supplement angle of

0%
$122.7^{\circ}$
0%
$131.7^{\circ}$
0%
$132.7^{\circ}$
0%
$132.4^{\circ}$

Explanation

Let the supplement be

$x$

Sum of supplementary angles is

$180^{\circ}$

$x+47.3^{\circ}=180^{\circ}$

$x=180^{\circ}-47.3^{\circ}=132.7^{\circ}$

The complementary angle of

$\displaystyle 30^{\circ}$ is:

0%
$\displaystyle 60^{\circ}$
0%
$\displaystyle 90^{\circ}$
0%
$\displaystyle 150^{\circ}$
0%
none of these

Explanation

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

Given, measure of one complementary angle is $30^o.$

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

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

Hence, option $A$ is correct.

If l

$\displaystyle \parallel$ m and m

$\displaystyle \parallel$ n then

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l $\displaystyle \parallel$ p
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l $\displaystyle \parallel$ q
0%
m $\displaystyle \parallel$ q
0%
l $\displaystyle \parallel$ n

Explanation

Given:

$l\parallel m$ and

$m\parallel n$

From the above figure we can see that there are three lines

$l,m$ and

$n$ and

$l\parallel m$ and

$m\parallel n$ .

From the figure it is clear that

$l$ is also paralle to

$n$ .

So,

$\text{D}$ is the correct option.

1924490_415900_ans_64345dc701874d8091d0cfa78917a04e.png

$\displaystyle 96^{0}$ is an example of-

0%
Acute
0%
Obtuse
0%
Right
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None of these

If two angles in a triangle are 75

$\displaystyle ^{\circ}$ and 95

$\displaystyle ^{\circ}$ then the third angle is__

0%
30 $\displaystyle ^{\circ}$
0%
20 $\displaystyle ^{\circ}$
0%
10 $\displaystyle ^{\circ}$
0%
40 $\displaystyle ^{\circ}$

Explanation

Because by angle sum property, the sum of angles is

$180^o$ .

Let n be the third angle.

$\therefore 75\displaystyle ^{\circ}$ + 95

$\displaystyle ^{\circ}$ + n = 180

$\displaystyle ^{\circ}$

$\displaystyle \Rightarrow$ n =10

$\displaystyle ^{\circ}$

$\displaystyle \therefore$ Third angle = 10

$\displaystyle ^{\circ}$

A line AB is parallel to the line CD. This is symbolically written as

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$\overleftrightarrow{AB} \neq \overleftrightarrow{CD}$
0%
$\overleftrightarrow{AB} = \overleftrightarrow{CD}$
0%
$\overleftrightarrow{AB} \perp \overleftrightarrow{CD}$
0%
$\overleftrightarrow{AB} || \overleftrightarrow{CD}$

Explanation

$\Rightarrow$ Line symbol is

$(\longleftrightarrow)$ .

$\Rightarrow$ Line

$AB$ can be written as

$\overleftrightarrow{AB}.$

$\Rightarrow$ Line

$CD$ can be written as

$\overleftrightarrow{CD}.$

$\Rightarrow$ A line

$AB$ parallel line

$CD$ can be written

$: \overleftrightarrow{AB}\parallel \overleftrightarrow{CD}.$

1367548_405705_ans_7902557e96244bcb81d15567bca99d8f.png

Example for a pair of parallel lines

0%
corners of a room
0%
railway track
0%
sides of a triangle
0%
none

The value of

$y$ in the given figure is _____

0%
$65$
0%
$85$
0%
$75$
0%
$80$

Explanation

Given,

$\angle ABC=115^{\circ}$

$\angle ABC$ and

$\angle CBD$ form linear pair.

So,

$\angle ABC+\angle CBD=180^{\circ}$

$\Rightarrow 115^{\circ}+y^{\circ}=180^{\circ}$

$\Rightarrow y^{\circ}=180^{\circ}-115^{\circ}$

$\Rightarrow y^{\circ}=65^{\circ}$

Hence, the value of

$y$ is

$65$ .

In the figure,

$\displaystyle PQ\parallel ST,\angle PQR={ 100 }^{ o }$ , and

$\displaystyle \angle RST={ 110 }^{ o }$ . Then

$\displaystyle \angle QRS$ is equal to

0%
$\displaystyle { 80 }^{ o }$
0%
$\displaystyle { 30 }^{ o }$
0%
$\displaystyle { 70 }^{ o }$
0%
$\displaystyle { 60 }^{ o }$

$\displaystyle 170^{0}$ is an example of-

0%
Acute
0%
Right
0%
Obtuse
0%
None of these

A pair of angles with a common vertex and common arm are called

0%
Adjacent angles
0%
Complementary
0%
Supplementary
0%
None

Which of the following are acute angles?

0%
a and c
0%
a and b
0%
c and d
0%
b and d

Explanation

From the figure it is clearly visible that 'a' and 'b' are acute angles which lies between

$\displaystyle { 0 }^{ o }$ to

$\displaystyle { 90 }^{ o }$ .

An angle that is

$\displaystyle { 1 }^{ o }$ less than right angle is:

0%
Reflex angle
0%
Straight angle
0%
Obtuse angle
0%
Acute angle

Explanation

Right angle measures

$\displaystyle { 90 }^{ o }$

$\displaystyle { 1 }^{ o }$ less of right angle =

$\displaystyle { 90 }^{ o }-{ 1 }^{ o }$

$\displaystyle { 89 }^{ o }$
Which is an acute angle.

Acute angle is the angle which is greater than

$\displaystyle { 0 }^{ o }$ and less than

$\displaystyle { 90 }^{ o }$ .

Obtuse angle is the angle which is greater than

$\displaystyle { 90}^{ o }$ and less than

$\displaystyle {180 }^{ o }$ .

Right angle is the angle which is equal to

$90^o$ .

Reflex angle is the angle which is greater than

$\displaystyle {180}^{ o }$ and less than

$\displaystyle {360 }^{ o }$ .

Range of an obtuse angle is:

0%
$[0˚, 90˚)$
0%
$(0˚, 90˚]$
0%
$[90˚, 180˚)$
0%
$(90˚, 180˚)$

Explanation

Acute angle is the angle which is greater than

$\displaystyle { 0 }^{ o }$ and less than

$\displaystyle { 90 }^{ o }$ .

Obtuse angle is the angle which is greater than

$\displaystyle { 90}^{ o }$ and less than

$\displaystyle {180 }^{ o }$ .

Right angle is the angle which is equal to

$90^o$ .

Reflex angle is the angle which is greater than

$\displaystyle {180}^{ o }$ and less than

$\displaystyle {360 }^{ o }$ .

If one angle at a point is reflex angle, the other at that point may be :

0%
Acute angle
0%
Obtuse angle
0%
Straight angle
0%
Acute or obtuse angle

Explanation

We know, the angle formed at a point is

$\displaystyle { 360 }^{ o }$ .

When one of angle is reflex, it range from

$\displaystyle { 180 }^{ o }$ to

$\displaystyle { 360 }^{ o }$ .

If angle is

$\displaystyle { 200 }^{ o }$ then the other angle is

$\displaystyle { 160 }^{ o }$ , i.e obtuse angle.

If one reflex angle is

$\displaystyle { 300 }^{ o }$ then other angle is

$\displaystyle { 60 }^{ o }$ i.e acute angle.

Hence, the option

$D$ is correct.

Which of the following is obtuse angle?

0%
Two right angles
0%
One and half right angles
0%
One right angle
0%
Half a right angle

Explanation

Right angle

$=90^{\circ}$

One and half right angle

$=\dfrac { { 90 }^{ \circ } }{ 2 } +{ 90 }^{ \circ }={ 135 }^{ \circ }$

which is greater than

$90^{\circ}$

So it is an obtuse angle .

Option

$B$ is correct.

The supplementary angle of an angle is one third of the angle. Then the angle and its supplement are __________.

0%
$135^o, 45^o$
0%
$60^o, 180^o$
0%
$120^o, 350^o$
0%
$60^o, 120^o$

Explanation

Let the angle is

$x$ , and its supplementary angle is

$\dfrac{1}{3}x$ .

We know that the sum of the supplementary angles is

$180^o$ , then

$x+\dfrac{1}{3}x=180^o\\ \Rightarrow \dfrac{4}{3}x=180$

$\Rightarrow x=\dfrac{180\times 3}{4}=135^o$

It's supplementary angle

$=\dfrac{135}{3}=45^o$

What is the range of reflex angle?

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Greater than zero but less than $\displaystyle { 90 }^{ o }$
0%
Greater than $\displaystyle { 90 }^{ o }$ but less than $\displaystyle { 180 }^{ o }$
0%
Greater than $\displaystyle { 180 }^{ o }$ but less than $\displaystyle { 360 }^{ o }$
0%
Equal to $\displaystyle { 360 }^{ o }$

Explanation

Acute angle is the angle which is greater than

$\displaystyle { 0 }^{ o }$ and less than

$\displaystyle { 90 }^{ o }$ .

Obtuse angle is the angle which is greater than

$\displaystyle { 90}^{ o }$ and less than

$\displaystyle {180 }^{ o }$ .

Right angle is the angle which is equal to

$90^o$ .

Now, by definition, reflex angle is the angle which is greater than

$\displaystyle {180}^{ o }$ and less than

$\displaystyle {360 }^{ o }$ .

That is, angles larger than a straight angle but less than

$1$ turn (between

$180^o$ and

$360^o$ ) are called reflex angles.

Therefore, the range of reflex angle is greater than

$180^o$ but less than

$360^o$ .

Hence, option

$C$ is correct.

Which of the following is a reflex angle?

0%
$\displaystyle { 180 }^{ o }$
0%
$\displaystyle { 360 }^{ o }$
0%
$\displaystyle { 204 }^{ o }$
0%
$\displaystyle { 135 }^{ o }$

Explanation

We know, reflex angle must be between

$\displaystyle { 180 }^{ o }$ and

$\displaystyle { 360 }^{ o }$ . It can't be equal to

$\displaystyle { 180 }^{ o }$ or

$\displaystyle { 360 }^{ o }$ as these are straight and complete angle, respectively.

Here, only

$204^o$ is greater than

$180^o$ and less than

$360^o$ .

Therefore, option

$C$ is correct.

Reflex angle is greater than _____ but less than _____angle.

0%
Complete, acute
0%
Acute, Straight
0%
Obtuse, Straight
0%
Straight, Complete

Explanation

Reflex angle is the angle which is greater than

$\displaystyle {180}^{ o }$ and less than

$\displaystyle {360 }^{ o }$ .

Straight angle is

$\displaystyle { 180 }^{ o }$ and complete angle is

$\displaystyle { 360 }^{ o }$ .

So reflex angle is greater than straight angle and less than complete angle.

Sum of two obtuse angle results in:

0%
Acute angle
0%
Right angle
0%
Obtuse angle
0%
Reflex angle

Explanation

Obtuse angle ranges from

$\displaystyle { 90 }^{ o }$ to

$\displaystyle { 180 }^{ o }$
So, sum of least obtuse angle is

$\displaystyle { 91 }^{ o }+{ 91 }^{ o }={ 182 }^{ o }$ , which is a reflex angle.
Now, sum of maximum obtuse angle is

$\displaystyle { 179 }^{ o }+{ 179 }^{ o }={ 358 }^{ o }$ , which is also a reflex angle.

Acute angle is the angle which is greater than

$\displaystyle { 0 }^{ o }$ and less than

$\displaystyle { 90 }^{ o }$ .

Obtuse angle is the angle which is greater than

$\displaystyle { 90}^{ o }$ and less than

$\displaystyle {180 }^{ o }$ .

Right angle is the angle which is equal to

$90^o$ .

Reflex angle is the angle which is greater than

$\displaystyle {180}^{ o }$ and less than

$\displaystyle {360 }^{ o }$ .

Which of the following is not an obtuse angle ?

0%
$\displaystyle { 127 }^{ o }$
0%
$\displaystyle { 149 }^{ o }$
0%
$\displaystyle { 175 }^{ o }$
0%
$\displaystyle { 182 }^{ o }$

Explanation

Acute angle is the angle which is greater than

$\displaystyle { 0 }^{ \circ }$ and less than

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

Obtuse angle is the angle which is greater than

$\displaystyle { 90}^{ \circ }$ and less than

$\displaystyle {180 }^{ \circ }$ .

Right angle is the angle which is equal to

$90^{\circ}$ .

Reflex angle is the angle which is greater than

$\displaystyle {180}^{ \circ }$ and less than

$\displaystyle {360 }^{ \circ }$ .

$\therefore \displaystyle { 182 }^{ \circ }$ is a reflex angle, so it is not an obtuse angle.

Find the measure of the missing angle in the triangle below.

0%
$35^o$
0%
$40^o$
0%
$45^o$
0%
$50^o$
0%
$55^o$

Explanation

By angle sum property, the sum of angles is

$180^o$ .

If we subtract the two given angles from

$180^0$ , the result will be the missing angle which is

$= 180^0 - 95^0 - 35^0 = 50^0$ .

Therefore, the missing angle is

$50^0$ .

If two angles are supplementary, then their sum is

0%
$90^o$
0%
$180^o$
0%
$270^o$
0%
$360^o$

Explanation

If two angles are supplementary , then their sum is

${ 180 ^o }$

If sum of two angles is

$\displaystyle { 90 }^{ o }$ . They will be:

0%
Linear pair
0%
Supplementary angles
0%
Complementary angles
0%
Corresponding angles

Explanation

By definition we know that two angles, the sum of whose measure is

${ 90^o }$ are called complimentary angles.

Then, such angles are called complement of each other.

E.g.: Let the measure of one complementary angle is

$58^o.$

$\Rightarrow$ Measure of other complementary angle $=90^o-58^o$ $=32^o.$

$\therefore$ Measure of the complementary angle of $58^{o}=32^o$ .

Hence, $58^{o}$ and $32^o$ are complements of each other.

That is, if the sum of two angles is $90^o$

Therefore, option $C$ is correct.

Two angles are supplementary, if one of them is

$\displaystyle { 49 }^{ o }$ . Find the other angle?

0%
$\displaystyle { 139 }^{ o }$
0%
$\displaystyle { 131 }^{ o }$
0%
$\displaystyle { 141 }^{ o }$
0%
$\displaystyle { 135 }^{ o }$

Explanation

Since, two angles are supplementary their sum is

$\displaystyle { 180 }^{ o }$

$\displaystyle \angle 1+\angle 2={ 180 }^{ o }$

$\displaystyle { 49 }^{ o }+\angle 2={ 180 }^{ o }$ (As one of the angle is

$\displaystyle { 49 }^{ o }$

$\displaystyle \angle 2={ 180 }^{ o }-{ 49 }^{ o }$

$\displaystyle ={ 131 }^{ o }$

In the figure aove,

$C$ is the intersection of

$\bar { AD }$ and

$\bar { BE }$ . If it can be determined, what is the measure of

$\angle BAC$ ?

0%
${80}^{o}$
0%
${100}^{o}$
0%
${110}^{o}$
0%
${115}^{o}$
0%
Cannot be determined from the given information

Explanation

$\angle BCA=\angle DCE$ (Vertically opposite angles)

$\Rightarrow \angle BCA=45^{\circ}$

Now in

$\triangle ABC$ using angle sum property

$\angle BAC+\angle CBA+\angle BCA=180^{\circ}$

$\Rightarrow \angle BAC+{ 35 }^{ \circ }+{ 45 }^{ \circ }={ 180 }^{ \circ }\\ \Rightarrow \angle BAC={ 180 }^{ \circ }-{ 80 }^{ \circ }\\ \Rightarrow \angle BAC={ 100 }^{ \circ }$

CBSE Questions for Class 9 Maths Lines And Angles Quiz 3 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Lines And Angles Quiz 3 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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