Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Assertion is correct but Reason is incorrect

Both Assertion and Reason are incorrect

MCQ Questions for Class 9 Maths Lines And Angles Quiz 9

In the given figure,

$AOB$ is a straight line and the ray

$OC$ stands on it. If

$\angle BOC=132^{o}$ , then

$\angle AOC=?$

0%
$68^{o}$
0%
$48^{o}$
0%
$42^{o}$
0%
None of these

Explanation

Given,

$\angle BOC=132^{o}$

$\angle AOC$ = ?

We can write,

$\angle AOC + \angle BOC$ =

$180^{o}$ ....

$[\because Linear\,pair]$

$\Rightarrow \angle AOC + 132^{o}$ =

$180^{o}$

$\Rightarrow \angle AOC$ =

$180^{o}-132^{o}$

$\Rightarrow \angle AOC$ =

$48^{o}$

Hence, the required answer is

$48^o$

Triangle DEF in figure is right triangle with

$\angle E=90^{o}$ .
What type of angles are

$\angle D$ and

$\angle F$ ?

0%
They are equal angles
0%
They form a pair of adjacent angles
0%
They are complementary angles
0%
They are supplementary angles

Explanation

$\angle D+\angle E+\angle F=180^{o}$ ....Angle sum property

$\because \angle E=90^{o}$

$\Rightarrow \angle D+\angle F=180^{o}-90^{o}$

$\Rightarrow \angle D+\angle F=90^{o}$
Therefore, angle

$D$ and

$F$ are complementary angles.

In the given figure,

$AOB$ is a straight line,

$\angle AOC$ =

$68^{o}$ and

$\angle BOC$ =

$x^{o}$ .Find x

0%
$32$
0%
$22$
0%
$112$
0%
$132$

Explanation

Because,
=

$\angle BOC + \angle AOC$ =

$180^{o}$ ....

$[\because Linear\,pair]$
=

$x^{o} + 68^{o}$ =

$180^{o}$
=

$x$ =

$180-68$
=

$x$ =

$112$

Angles which are both supplementary and vertically opposite are

0%
$95^o , 85^o$
0%
$90^o, 90^o$
0%
$100^o, 80^o$
0%
$45^o, 45^o$

Explanation

As we know, vertically opposite angles are equal.
Let the angle be

$y$

$\Rightarrow y+y=180^o$

$\Rightarrow 2y=180^o$

$\Rightarrow y=90^o$
Therefore,

$90^o$ is asked angle for each.

Angles between South & West and South & East are

0%
vertically opposite angles
0%
complementary angles
0%
making a linear pair
0%
adjacent but not supplementary

Explanation

We have,

Angle between South and West

$=90^o$

Angle between South and East

$=90^o$

Sum of the angles

$=180^o$

$\therefore$ The angles between South and West and South and East are making a linear pair.

Hence, option (C) is correct.

1671819_1789943_ans_4953d13cefb24f19b32a56cc2367eee9.png

If the complement of an angle is

$79^o$ , then the angle will be of :

0%
$1^o$
0%
$11^o$
0%
$79^o$
0%
$101^o$

Explanation

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

Given, measure of one complementary angle is $79^o.$

$\Rightarrow$ Measure of other complementary angle $=90^o-79^o$ $=11^o.$

$\therefore$ Measure of a complementary angle of $79^{o}=11^o$ .

Hence, option $B$ is correct.

In figure,

$PQ$ is a mirror,

$AB$ is the incident ray and

$BC$ is the reflected ray. If

$\angle ABC=46^o$ , then

$\angle ABP$ is equal to

0%
$44^o$
0%
$67^o$
0%
$13^o$
0%
$62^o$

Explanation

Given

$\angle ABC=46^o$

We know that in a plane mirror,

the angle of the incident

$=$ angle of reflection.

$\Rightarrow \angle CBQ =\angle ABP\quad...(i)$

Since,

$PQ$ is straight line

$\therefore \angle ABP +\angle ABC+\angle CBQ =180^o$

$\Rightarrow \angle ABP +\angle ABC +\angle ABP =180^o\qquad$ [from

$(i)$ ]

$\Rightarrow 2\angle ABP +46^o =180^o$

$\Rightarrow 2\angle ABP =180^o -46^o =134$

$\Rightarrow \angle ABP =\dfrac{134^o}{2}$

$\Rightarrow \angle ABP =67^o$

Hence, option (B) is correct.

The angles between North & West and South & East are

0%
complementary
0%
supplementary
0%
both are acute
0%
both are obtuse

Explanation

Option (b) is correct.

The angle between the North and West

$=90^o$

The angle between the South and East

$=90^o$

Therefore, the angle between North & West and South & East are supplementary angles as they add up to

$180^o$ .

1671809_1789938_ans_e63ced7186df41bb8333790fc019ab69.png

In figure,

$POQ$ is a line. If

$x=30^o$ , then

$\angle QOR$ is

0%
$90^o$
0%
$30^o$
0%
$150^o$
0%
$60^o$

Explanation

Option (a) is correct.
It has been given that

$POQ$ is a straight line.

$\therefore x+2y+3y=180^o$

$\Rightarrow 5y+30^o =180^o$

$\Rightarrow 5y=180^o -30^o$

$\Rightarrow y=\dfrac{150^o}{5}$

$\Rightarrow y=30^o$

$\because \angle QOR =3y$

$\therefore QOR=3\times 30^o$

$\Rightarrow \therefore \angle QOR=90^o$

The angle which makes a linear pair with an angle of

$61^\circ$ is of

0%
$29^\circ$
0%
$61^\circ$
0%
$122^\circ$
0%
$119^\circ$

Explanation

Let the angle making linear pair with

$61^\circ$ be

$y$ . Then,

$y+61^\circ =180^\circ$ [Given as linear pair]

$\Rightarrow y=180^\circ -61^\circ$

$\Rightarrow y=119^\circ$

Hence, option

$D$ is correct.

In figure, lines

$l$ and

$m$ intersect each other at a point. Which of the following is false?

0%
$\angle a= \angle b$
0%
$\angle d =\angle c$
0%
$\angle a+ \angle d=180^o$
0%
$\angle a=\angle d$

Explanation

The two lines

$l$ and

$m$ shown in the figure forms

$4$ angles,

$a,\ b,\ c\ and\ d$ .

$\angle a$ and

$\angle b$ are vertically opposite angles.

Hence,

$\angle a=\angle b$ .

Similarly,

$\angle c$ and

$\angle d$ are also vertically opposite angles.

Hence,

$\angle d=\angle c$ .

Also,

$\angle a$ and

$\angle d$ form a linear pair.

Hence,

$\angle a+\angle d=180^o$

Since

$\angle a+\angle d=180^o$ ,

$\angle a$ cannot be equal to

$\angle d$ , unless they are both right angles, which is not the case here.

Hence, option D is false here.

In figure, the value of

$x$ is

0%
$110^o$
0%
$46^o$
0%
$64^o$
0%
$150^o$

Explanation

Option (d) is correct.
As we knew, the angle made around a point is

$360$ degree.
Then,

$\therefore y+64^o +46^o +100^o -360^o$

$\Rightarrow y+210^o =360^o$

$\Rightarrow y=360^o -210^o$

$\Rightarrow y=150^o$

In figure, the value of

$y$ is

0%
$30^o$
0%
$15^o$
0%
$20^o$
0%
$22.5^o$

Explanation

Option (c) is correct.
All the angle lies on the straight line.

$\therefore 6y+y+2y=180^o$

$\Rightarrow 9y=180^o$

$\Rightarrow y=\dfrac{180^o }{9}$

$\Rightarrow y=20^o$

In figure,

$POR$ is a line. The value of

$a$ is

0%
$40^o$
0%
$45^o$
0%
$55^o$
0%
$60^o$

Explanation

Option (a) is correct.
It has been given that

$POR$ is a straight line.

$\therefore \angle POQ +\angle QOR =180^o$

$\Rightarrow (3a+5)^o +(2a-25)^o =180^o$

$\Rightarrow 5a=180^o +20^o =200^o$

$\Rightarrow a=\dfrac{200^o}{5}$

$\Rightarrow a=40^o$

The angles

$x$ and

$90^o -x$ are:

0%
supplementary
0%
complementary
0%
vertically opposite
0%
making a linear pair

Explanation

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

Sum of given angles = $(90^o-x^o)+$ $x^o=90^o$ .

Hence, these are complementary angles.

Therefore, option $B$ is correct.

The angles

$x-10^o$ and

$190^o-x$ are

0%
interior angles on the same side of the transversal
0%
making a linear pair
0%
complementary
0%
supplementary

Explanation

Option (d) is correct.

Given that

$x-10^o+190^o-x$

$\Rightarrow 190^o -10^o$

$\Rightarrow180^o$

Therefore, given angles are supplementary.

0%
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
0%
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
0%
Assertion is correct but Reason is incorrect
0%
Both Assertion and Reason are incorrect

Explanation

When a transversal intersects two parallel lines, the angle made on the interior same side is

$180$ degrees.

So, both are facts but reason does not explain assertion correctly.

Hence, option

$B$ is correct.

If two supplementary angles are in the ratio

$1:2$ , then the bigger angle is

0%
$120^o$
0%
$125^o$
0%
$110^o$
0%
$90^o$

Explanation

Option

$(A)$ is correct.

Two supplementary angles are in the ratio

$1:2$

So, let two angles be

$x$ and

$2x$

Given that, angles are supplementary

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

$\Rightarrow 3x=180$

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

$\Rightarrow x=60^o$

Therefore, bigger angle is

$2x=120^{\circ}.$

In figure,

$\angle AOC$ and

$\angle BOC$ form a pair of

0%
vertically opposite angles.
0%
complementary angles.
0%
alternate interior angles.
0%
linear pair of angles.

Explanation

In figure,

$\angle AOC$ and

$\angle BOC$ lie on a straight line and on the same side of the straight line.

So, they form a linear pair of supplementary angles that is

$\angle AOC+\angle BOC=180^{\circ}$ .

Hence, option

$(D)$ is correct.

One obtuse angle and one acute angle can make a pair of complementary angels.

0%
True
0%
False

Explanation

We know, two angles are complementary when they add up to

$90^o$ .

But one obtuse angle is already greater than

$90^o$ .

Hence, the sum of an obtuse and an acute angle is obviously greater than

$90^o$ .

That is, the given statement is false.

Therefore, option

$B$ is correct.

One obtuse angle and one acute angle can make a pair of supplementary angles.

0%
True
0%
False

Explanation

let,

$A=120^0$ be obtuse angle and

$B=60^0$ be acute angle.

So,

$A+B=180^0$

That means

$A$ (obtuse angle) and

$B$ (acute angle) are supplementary

So, given statement is true

In figure, the value of

$a$ is

0%
$20^o$
0%
$15^o$
0%
$5^o$
0%
$10^o$

Explanation

Option

$(D)$ is correct.

$\Rightarrow \angle AOF =COD$ [ vertically opposite angles ]

$\therefore \angle COD =90^o$

Now,

$\angle BOC+\angle COD+\angle EOD=180^{\circ}\cdots\cdots[\because\text{making linear pair}]$

$\Rightarrow 40^o +90^o +5a=180^o$

$\Rightarrow 5a+130^o =180^o$

$\Rightarrow 5a=180^o-130^o$

$\Rightarrow 5a=50^o$

$\Rightarrow a=10^o$

1667812_1790105_ans_54b4387485a0404c857dd3d362616e9c.png

0%
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
0%
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
0%
Assertion is correct but Reason is incorrect
0%
Both Assertion and Reason are incorrect

Explanation

As we see,

$\angle AOC$ and

$\angle BOC$ have a common vertex

$O$ . So,

$a$ and

$b$ are adjacent angles

And

$OB$ and

$OA$ are opposite rays.

So,

$a$ and

$b$ are linear pair that means their sum is

$180^{\circ}$ .

But, adjacent angles does not necessarily add up to give

$180^{\circ}$ , it can give any sum.

So, reason is not correct explanation.

Hence, option

$B$ is correct.

$40^o$ is the complement of

$60^o$ ?

0%
True
0%
False

Explanation

We know, two angles whose sum is equal to

$90^o$ are known as complementary angles.

Given, the angles are

$40^o$ and

$60^o$ .

Then their sum

$=40^o+60^o=100^o\ne90^o$ .

Hence, the angles are not complementary.

Therefore, the statement is false.

Hence, option

$B$ is correct.

$45^o$ is the supplement of

$45^o$ ?

0%
True
0%
False

Explanation

$45^0$ is the supplement of

$135^0$ not

$45^0$

The difference of two complementary angles is

$30^o$ . Then, the angles are:

0%
$60^o, 30^o$
0%
$70^o, 40^o$
0%
$20^o, 50^o$
0%
$105^o, 75^o$

Explanation

Let

$x$ and

$y$ be the angles.
Then,

$x+y=90^o ....(1)$ [ Complementary angle]
Also,

$x-y=30^o ....(2)$ [ Given ]
By addition of both equations, we get,

$\Rightarrow 2x=120^o$

$\Rightarrow x=\dfrac{120^o}{2}$

$\Rightarrow x=60^o$ .
Putting the value of

$x$ in equation

$(1)$ , we get,

$\Rightarrow 60+y=90^o$

$\Rightarrow y=90^o -60^o$

$\Rightarrow y=30^o$
Therefore, the required angles are

$30^o$ and

$60^o$ .

Hence, option

$A$ is correct.

Two right angle are complementary to each other.

0%
True
0%
False

Explanation

We know, two angles are complementary when they add up to

$90^o$ .

But two right angles add up to

$180^{\circ}$ that is they are supplementary to each other.

Therefore, the given statement is

$False$ .

In figure,

$a$ and

$b$ are :

0%
alternate exterior angles
0%
corresponding angles
0%
alternate interior angles
0%
vertically opposite angles

Explanation

Here,

$m$ and

$n$ are the straight lines and transversal

$l$ intersects both the lines

$m$ and

$n$ .

Therefore, the angle

$a$ and

$b$ are alternate angles because of their position, that is, in the opposite side of the transversal and they are both lying on inside of a region covered by line

$m$ and

$n$ .

So, they are alternate interior angles.

Hence, option

$(C)$ is correct.

In figure, lines

$PQ$ and

$ST$ intersect at

$O$ . If

$\angle POR=90^o$ and

$x:y =3:2$ , then

$z$ is equal to

0%
$126^o$
0%
$144^o$
0%
$136^o$
0%
$154^o$

Explanation

We can see in the given figure,

$PQ$ is a straight line

$\therefore \angle POR +ROT +\angle TOQ =180^o$

$\Rightarrow 90^o +x+y=180^o$

$\Rightarrow x+y=90^o$

$\Rightarrow x+y=90^o$ ...(1)

Given that,

$\dfrac xy =\dfrac 32$

Let

$x=3K$ and

$y=2K$

From equation (1)

$\Rightarrow 3K+2K=90^o$

$\Rightarrow K=\dfrac{90^o}{5}$

$\Rightarrow K=18^o$

$\therefore y=2\times 18^o =36^o$

Now,

$SOT$ is a straight line

$\Rightarrow z+y=180^o$

$\Rightarrow z+36^o =180^o$

$\Rightarrow z=180^o-36^o$

$\Rightarrow z=144^o$

Hence, Option

$(B)$ is correct.

Two angles making a linear pair are always adjacent angles.

0%
True
0%
False

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

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Practice Class 9 Maths Quiz Questions and Answers

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

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Practice Class 9 Maths Quiz Questions and Answers

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