MCQ Questions for Class 9 Maths Lines And Angles Quiz 7

Which of the following are complementary angles?

0%
$71^o$ and $19^o$
0%
$18^o$ and $180$
0%
$90^o$ and $90^o$
0%
$90^o$ and $45^o$
0%
$15^o$ and $30^o$

What is the measure of angle B in the following figure if angle A measures

$135^o$ ?

0%
$40^o$
0%
$45^o$
0%
$50^o$
0%
$135^o$

In quadrilateral

$PQRS$ above, for what value of

$x$ ,

$PS\parallel QR$ ?

0%
$158$
0%
$132$
0%
$120$
0%
$110$
0%
$70$

Explanation

It is given that

$PS || QR$ .

Also,

$\angle SPQ=70^{0}$

$PQ$ acts as a transversal since

$PS||QR$ .

Hence,

$\angle SPQ +\angle RQP=180^{0}$

$\Rightarrow 70^{0}+\angle Q=180^{0}$

$\Rightarrow \angle Q=110^{0}$

Hence, the value of

$x$ is

$110$ .

In the figure, if

$\angle q=140$ , what is the value of

$\angle r- \angle p$ ?

0%
$0^o$
0%
$10^o$
0%
$90^o$
0%
$130^o$

Explanation

Angles

$p$ and

$q$ form a linear pair as seen in the figure.

Since

$\angle q = 140^o, \angle p = 180^o-40^o=40^o$ .

Also, the angle vertically opposite to

$p$ in the right angled triangle will also be equal to

$p=40^o$ .

Since

$\angle r$ is the exterior angle of the given right angled triangle,

$r = 90^o + 40^o = 130^o$

$\therefore \angle r - \angle p = 90^o$ .

Hence, option

$C$ is correct.

Find the complement of each of the following angles

$24^{\circ}$ .

0%
$66^{\circ}$
0%
$156^{\circ}$
0%
$36^{\circ}$
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 $24^o.$

$\Rightarrow$ Measure of other complementary angle $=90^o-24^o$ $=66^o.$

$\therefore$ Measure of a complementary angle of $24^{o}=66^o$ .

Therefore, option $A$ is correct.

In the adjacent figure PQ || ST,

$\angle PQR = 110^o$ and

$\angle RST = 130^o$ , find

$\angle QRS$ .

0%
$30^o$
0%
$130^o$
0%
$60^o$
0%
$160^o$

Explanation

Draw a line $XY$ parallel to ${{PQ}}\parallel {{ST}}$ .

It is known that the sum of interior angles on the same side of the transversal is $180^\circ$ .

So, $\angle {{PQR}} + \angle {{QRX}} = 180^\circ$

$110^\circ + \angle {{QRX}} = 180^\circ$

$\angle {{QRX}} = 70^\circ$

Similarly,

$\angle {{RST}} + \angle {{SRY}} = 180^\circ$

$130^\circ + \angle {{SRY}} = 180^\circ$

$\angle {{SRY}} = 50^\circ$

Now, by property of linear pair,

$\angle {{QRX}} + \angle {{QRS}} + \angle {{SRY}} = 180^\circ$

$70^\circ + \angle {{QRS}} + 50^\circ = 180^\circ$

$\angle {{QRS}} = 60^\circ$

Find the supplement of the following angle.

$40^{\circ}$

0%
$140$
0%
$40$
0%
$10$
0%
None of these

Explanation

We know that the supplement angle

$=180^0-\theta$

So,

The supplement angle of

$40^0$ will be

$=180^0-40^0=140^0$

Hence, this is the answer.

Write 'True' or 'False'.
A straight angle measures

$90^o$

0%
True
0%
False

Explanation

Given

$\rightarrow$ A straight angle measures

$90^{\circ}$

To find

$\rightarrow$ Whether the given statement is true or false.

A straight angle measures

$180^{\circ}$ . In radian it is measured as

$\pi$ angle.

Therefore, the given statement is false.

Correct option is B.

2107935_700752_ans_a93bd2276c144de19eb02edf30729a5b.png

Find the complement of each of the following angles

$20^{\circ}$ .

0%
$70^{\circ}$
0%
$60^{\circ}$
0%
$110^{\circ}$
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 $20^o.$

$\Rightarrow$ Measure of other complementary angle $=90^o-20^o$ $=70^o.$

$\therefore$ Measure of a complementary angle of $20^{o}=70^o$ .

Therefore, option $A$ is correct.

Find the complement of each of the following angles

$48^{\circ}$ .

0%
$42^{\circ}$
0%
$52^{\circ}$
0%
$132^{\circ}$
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 $48^o.$

$\Rightarrow$ Measure of other complementary angle $=90^o-48^o$ $=42^o.$

$\therefore$ Measure of a complementary angle of $48^{o}=42^o$ .

Therefore, option $A$ is correct.

Two angles are equal and supplementary to each other. find them.

0%
$90^0 , \, 90^0$
0%
$30^0 , \, 150^0$
0%
$45^0 , \, 45^0$
0%
None of these

Explanation

$\textbf{Step 1: Find angles using the sum of supplementary angles.}$

$\text{Let, } x, x\text{ be two angles}$

$\text{Now,}$

$x+x=180^\circ$

$[\textbf{Sum of supplementary angles }\boldsymbol{=180^\circ}]$

$\Rightarrow 2x=180^\circ$

$x=90^\circ$

$\textbf{Hence, Option A is correct.}$

Find the complement of each of the following angles

$35^{\circ}$ .

0%
$55^{\circ}$
0%
$145^{\circ}$
0%
$35^{\circ}$
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 $35^o.$

$\Rightarrow$ Measure of other complementary angle $=90^o-35^o$ $=55^o.$

$\therefore$ Measure of a complementary angle of $35^{o}=55^o$ .

Therefore, option $A$ is correct.

As shown in the given figure, according to corresponding angle theorem, which two angles are equal?

0%
$\angle 1$ and $\angle2$
0%
$\angle 1$ and $\angle3$
0%
$\angle 1$ and $\angle4$
0%
$\angle 1$ and $\angle5$

Explanation

We have

$l||m$ and

$t$ is a transversal line which cuts

$l$ and

$m$ .

Then, in this given figure according to corresponding angle theorem,

$\angle1=\angle 5,\\ \angle 2=\angle 6,\\ \angle 3=\angle 7$

and

$\angle 4=\angle 8$ .

Hence, option

$D$ is correct.

As shown in above figure which of the following angles are equal

0%
$\angle1$ and $\angle2$
0%
$\angle1$ and $\angle3$
0%
$\angle1$ and $\angle4$
0%
None of the above

Explanation

As we can see in the figure, both lines are diagonals of given rectangle.

So, we can say that

$\angle 2=\angle 4$ and

$\angle 1=\angle 3$ [opposite angles]

What is the value of

$a-b$

0%
$180^0$
0%
$60^0$
0%
$70^0$
0%
$120^0$

Explanation

From figure, we can say

$\angle a=120^0$

and

$\angle b=60^0$ ....Vertically opposite angles

Thus

$a-b=120-60=60^0$

What is the measure of supplementary angle of

$108^{\circ}$ ?

0%
$76^{\circ}$
0%
$62^{\circ}$
0%
$72^{\circ}$
0%
$82^{\circ}$

What is the measure of complementary angle of

$12^{\circ}$ ?

0%
$68^{\circ}$
0%
$78^{\circ}$
0%
$88^{\circ}$
0%
$72^{\circ}$

In the given figure, AB

$||$ CD and BC

$||$ DE, then the value of x is _____________.

0%
$95^o$
0%
$90^o$
0%
$85^o$
0%
$80^o$

Explanation

$\angle ABC=\angle BCD=85^\circ (\because AB||CD)$

And

$\angle EDC=180-\angle BCD (\because BC||DE)$

$\Rightarrow x=180-85=95^\circ$

The measure of complementary angle of

$64^{\circ}$ is

$26^{\circ}$ .

0%
True
0%
False

Explanation

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

Given, measure of one complementary angle is $64^o.$

$\Rightarrow$ Measure of other complementary angle $=90^o-64^o$ $=26^o.$

$\therefore$ Measure of a complementary angle of $64^{o}=26^o$ .

Hence, the given statement is true.

Therefore, option $A$ is correct.

$l ||m$ and CD is transversal,

$\angle 1$ and

$\angle 2$ represents _____

0%
Co-interior angles
0%
Corresponding angles
0%
Alternate interior angles
0%
Exterior angles

Explanation

$\angle 1$ and

$\angle 2$ are alternate interior angles.

How many angles are less than

$90^o$ inside the given figures?

0%
$2$
0%
$3$
0%
$4$
0%
$5$

Explanation

Given,

Refer Fig.

Here

$\angle ABF,\angle BFC$ and

$\angle FCD$ is less than

$90^0$ .

So total

$3$ angles are

$<90^0$

option B is correct.

2108039_722812_ans_20257a4d6e2f49c7a80b1b902420136f.png

If measure of one angle of linear pair is

$102^{\circ}$ , then the measure of second angle is

$78^{\circ}$ .

0%
True
0%
False

Explanation

Sum of angles of linear pair is

$180°$ .

Hence if one angle of linear pair is

$102°$ , then the other angle will be:

$\implies 180°-102°=78°$ .

So above statement is true.

In the given figure,

$\angle QPB$ is

0%
${ 60 }^{ o }$
0%
${ 45 }^{ o }$
0%
${ 30 }^{ o }$
0%
${ 15 }^{ o }$

Explanation

$2x+3x+x=180^o(\text{linear pair})$

$6x=180^o$

$x=30^o$

Lines

$PQ$ and

$RS$ intersect at

$O$ . If

$\angle POS=2\angle SOQ$ then the four angles at

$O$ are

0%
${ 30 }^{ o },{ 30 }^{ o },{ 120 }^{ o },{ 180 }^{ o }$
0%
${ 60 }^{ o },{ 60 }^{ o },{ 120 }^{ o },{ 120 }^{ o }$
0%
${ 60 }^{ o },{ 90 }^{ o },{ 90 }^{ o },{ 120 }^{ o }$
0%
${ 30 }^{ o },{ 60 }^{ o },{ 90 }^{ o },{ 180 }^{ o }$

Explanation

$x+2x=180 (linear pair)\Rightarrow x={ 60 }^{ o }\Rightarrow \angle SOP={ 120 }^{ o }$

$\therefore \text{four angle are at O}\quad are\ { 60 }^{ o },{ 60 }^{ o },{ 120 }^{ o },{ 120 }^{ o }\quad$

The angle between two opposite rays is ________.

0%
Right
0%
Obtuse
0%
Acute
0%
Straight

Which of the following is an obtuse angle?

0%
$92^{\circ}$
0%
$181^{\circ}$
0%
$195^{\circ}$
0%
$83^{\circ}$

A transversal intersects two or more than two lines at _________ points.

0%
Same
0%
Different
0%
Equidistant
0%
None of these

Find the value of x, y and z in the adjoining figure.

0%
$x=160$ , $y=60$ , $z=80$
0%
$x=60$ , $y=80$ , $z=40$
0%
$x=80$ , $y=60$ , $z=140$
0%
$x=140$ , $y=80$ , $z=60$

Explanation

$In\triangle BCE$

$\implies\quad \angle BEC+\angle BCE+\angle CBE={ 180 }^{ \circ }$

$\implies\quad { 90 }^{ \circ }+{ 30 }^{ \circ }+\angle CBE={ 180 }^{ \circ }$

$\implies\quad \angle CBE={ 60 }^{ \circ }$

$y={ 60 }^{ \circ }$

$In\triangle APC:$

$\implies\quad { 50 }^{ \circ }+{ 30 }^{ \circ }+\angle APC={ 180 }^{ \circ }$

$\implies\quad \angle APC={ 100 }^{ \circ }$

$\therefore x=180-\angle APC$

$(\because sum\quad of\quad angles\quad on\quad a\quad straight\quad line={ 180 }^{ \circ })$

$\implies\quad x={ 180 }^{ \circ }-{ 100 }^{ \circ }={ 80 }^{ \circ }$

$In\triangle BOP:$

$z=x+y\quad (exterior\quad angle\quad of\quad a\quad triangle=sum\quad of\quad two\quad opposite\quad interior\quad angles)$

$\implies\quad z=80+60={ 140 }^{ \circ }$

$\therefore x={ 80 }^{ \circ }\quad ,\quad y={ 60 }^{ \circ }\quad ,z={ 140 }^{ \circ }$

1005693_1068116_ans_2962fefc78cf4968a64e0b6d4848aa0e.png

$\triangle ABC,\angle A={ x }^{ \circ },\angle B={ \left( 2x-15 \right) }^{ \circ}$ and

$\angle C ={ \left( 3x+21 \right) }^{ \circ }$ . Find the value of

$x$ and the measure of each angle of the triangle.

0%
$x={ 27 }^{ \circ },\angle A={ 27 }^{ \circ },\angle B={ 41 }^{ \circ },\angle C={ 101 }^{ \circ }$
0%
$x={ 29 }^{ \circ },\angle A={ 29 }^{ \circ },\angle B={ 43 }^{ \circ },\angle C={ 108 }^{ \circ }$
0%
$x={ 27 }^{ \circ },\angle A={ 27 }^{ \circ },\angle B={ 41 }^{ \circ },\angle C={ 108 }^{ \circ }$
0%
$x={ 30 }^{ \circ },\angle A={ 30 }^{ \circ },\angle B={ 41 }^{ \circ },\angle C={ 109 }^{ \circ }$

Explanation

Given,

$\angle A=x^\circ$ ,

$\angle B=(2x-15)^\circ$ and

$\angle C=(3x+21)^\circ$ .

We know, by angle sum property, the sum of angles of a triangle is

$180^\circ$ .

Then,

$\angle A+ \angle B+ \angle C=180^\circ$

$\implies$

$x^\circ+(2x-15)^\circ+ (3x+21)^\circ=180^\circ$

$\implies$

$6x^\circ+6^\circ=180^\circ$

$\implies$

$6x^\circ=180^\circ-6^\circ$

$\implies$

$6x^\circ=174^\circ$

$\implies$

$x^\circ=29^\circ$ .

Therefore,

$\angle A=x^\circ=29^\circ$ ,

$\angle B=(2x-15)^\circ=2\times29^\circ-15^o=58^\circ-15^\circ=43^\circ$

and

$\angle C=(3x+21)^\circ=3\times29^\circ+21^\circ=87^\circ+21^\circ=108^\circ$ .

Hence, option

$B$ is correct.

From the figure, find values of

$x$ and

$y$ .

0%
$25^{o},30^{o}$
0%
$35^{o},31^{o}$
0%
$50^{o},28^{o}$
0%
$45^{o},33^{o}$

Explanation

In the given triangle,

by angle sum property,

$40^o+95^o+x^o=180^o.......(i)$

and

$x^o+y^o+102^o=180^o.......(ii)$ .

From

$(i)$ ,

$40^o+95^o+x^o=180^o$

$\implies$

$135^o+x^o=180^o$

$\implies$

$x^o=180^o-135^o$

$\implies$

$x^o=45^o.......(iii)$ .

Substitute

$(iii)$ in

$(ii)$ ,

$45^o+y^o+102^o=180^o$

$\implies$

$y^o+147^o=180^o$

$\implies$

$y^o=180^o-147^o$

$\implies$

$y^o=33^o$ .

Therefore,

$x^o=45^o$ and

$y^o=33^o$ .

Hence, option

$D$ is correct.

CBSE Questions for Class 9 Maths Lines And Angles Quiz 7 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Lines And Angles Quiz 7 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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