MCQ Questions for Class 9 Maths Lines And Angles Quiz 2

With respect to the figure, write all pairs of adjacent angles and all the linear pairs.

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Adjacent angles: $\angle AOD \ \ \& \ \ \angle COD$
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Adjacent angles: $\angle BOC \ \ \& \ \ \angle COD$
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Linear pairs: $\angle AOD \ \ \& \ \ \angle BOD$
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Linear pairs: $\angle AOC \ \ \& \ \ \angle BOC$

Explanation

$Adjacent\quad angles\quad are\quad those\quad angles\quad which\quad have\quad common\quad side\quad and\quad common\quad vertex.\\ Hence\quad \angle AOD\quad and\quad \angle COD\quad are\quad adjacent.(Common\quad side\quad OD\quad and\quad common\quad vertex\quad O)\\ \angle BOC\quad and\quad \angle COD\quad are\quad adjacent\quad (Common\quad side\quad OC\quad and\quad common\quad vertex\quad O)\\ Linear\quad pair\quad of\quad angles\quad are\quad angles\quad which\quad add\quad up\quad to\quad form\quad 180\quad \\ \angle AOD\quad and\quad \angle BOD\quad form\quad linear\quad pair\\ \angle AOC\quad and\quad \angle BOC\quad form\quad linear\quad pair$

Find the measure of the complementary angle of each of

$20^o$ .

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$50^o$
0%
$70^o$
0%
$160^o$
0%
$80^o$

Explanation

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

Given, measure of one complementary angle is $= 20^{\circ}$ .

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

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

Therefore, option $B$ is correct.

Find the measure of the supplementary angle of

$132^o$

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$48^o$
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$32^o$
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$42^o$
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$38^o$

Explanation

Two angles are Supplementary when their sum is equal to

$180^{\circ}$ .

If one angle

$= 132^{\circ}$ , let the other angle be

$x$ .

Hence,

$x + 132^{\circ} = 180^{\circ}$

$x = 180^{o} - 132^o \\= 48^o$

Hence, supplementary angle of

$132^o$ is

$48^o$ .

A ray stands on a line, then the sum of the two adjacent angles so formed is ______.

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$180^\circ$
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$90^\circ$
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$360^\circ$
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$270^\circ$

Explanation

If a ray stands on a line, then the sum of two adjacent angles so formed is equal to $180^\circ$ which is also known as a linear pair.

Based on the angle measures given, which triangle is not acute?

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$35^\circ,\, 69^\circ,\, 76^\circ$
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$60^\circ,\, 60^\circ,\, 60^\circ$
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$88^\circ,\, 46^\circ,\, 46^\circ$
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$90^\circ,\, 45^\circ,\, 45^\circ$

Explanation

For acute angles triangle all the three angles must be less than

${ 90 }^{ \circ }$ .

In option

$D$ one of the angle is

${ 90 }^{ \circ }$ , so it is not acute angles triangle.

Based on the given figure, which of the following statements is true?

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$\angle\, 5$ and $\angle\, 7$ are supplementary angles.
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$\angle\, 7\, =\, 55^\circ$
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$\angle\, 8$ and $\angle\, 1$ are corresponding angles.
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$\angle\, 4$ and $\angle\, 5$ are alternate angles.

Explanation

$\angle 5$ and

$\angle 7$ are vertically opposite angles.

$\angle 6=55^{\circ}$ (Alternate angles)

$\angle 7+\angle 6=180^{\circ}$ (Adjacent angle on straight line)

$\Rightarrow \angle 7+{ 55 }^{ \circ }={ 180 }^{ \circ }\\ \Rightarrow \angle 7={ 125 }^{ \circ }$

$\angle 1$ and

$\angle 8$ are not corresponding angles.

$\angle 4$ and

$\angle 5$ are alternate angles.

So only option

$D$ is correct.

An exterior angle of a triangle is equal to the sum of two ______ opposite angles.

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interior
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exterior
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vertical
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none of these

Explanation

Consider the given triangle, we can easily apply exterior angle property of triangle.

For given triangle $XYZ$ ,

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

Also, $\angle 3+\angle z=180^{o}$ ......... (Linear pair of angles)

$\angle 1+\angle 2+\angle z=\angle 3 +\angle z$

$\Rightarrow \angle 3=\angle 1+\angle 2$ ...... (which is the Exterior angle property).

Therefore, we can say that, an exterior angle of a triangle is equal to the sum of the two interior opposite angles.

Hence, option $A$ is correct.

1958626_243409_ans_87aeb76af5394377b454d787a0d74421.png

Find the measure of the complementary angle of

$90^\circ$ .

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$0^\circ$
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$45^\circ$
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$90^\circ$
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$60^\circ$

Explanation

The pair of angles is said to be complementary, when their sum is

$90^{o}$ .

Let

$x,y$ be any two complementary angles and

$(\angle x)=90^{o}$

$\implies (\angle x)+(\angle y)=90^{o}$ ........ (By definition of complementary angles)

$\implies 90^{o}+(\angle y)=90^{o}$

$\implies (\angle y)=0^{o}$ .

Hence, measure of complementary angle of

$90^{o}$ is

$0^{o}$ .

Hence, option

$A$ is correct.

If an angle is

$28^o$ less than its complement, find its measure.

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$31^o$
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$131^o$
0%
$28^o$
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$32^o$

Explanation

Let the required angle be

$x$ .

Then, its complement

$=(90^o-x)$ .

Given, the angle is

$28^o$ less than its complement.

Then,

$x=(90^o-x)-28^o$

$\Rightarrow x+x=90^o-28^o$

$\Rightarrow 2x=62^o\\ \Rightarrow x=\dfrac { 62 }{ 2 } ^o\\ \Rightarrow x={ 31 }^{ o }$ .

Therefore, option

$A$ is correct.

One of the angles of a triangle is

$65^o$ . Find the remaining two angles, if their difference is

$25^o$ .

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$70^o, 45^o$
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$55^o, 40^o$
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$50^o, 85^o$
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$75^o, 40^o$

Explanation

Let one angle be

$\angle x$

$\therefore$ other angle is

$\angle x+25^o$
Now,
We know, by angle sum property, the sum of all angles of a triangles is

$180^0$ .

$\implies x+x+25^o+65^o=180^o$

$\implies 2x=180^o-90^o$

$\implies x=45^o$
Thus, the angles are

$45^o$ and

$70^o$

$\displaystyle \angle AOB$ is a / an _____________ angle.

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acute
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right
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obtuse
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none of these

Explanation

An obtuse angle is one which measures more than

$90^o$ but less than

$180^o$ .

OA and OB are opposite rays.

$x=75^o$ , what is the value of y?

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$105^o$
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$75^o$
0%
$45^o$
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$15^o$

Explanation

Sum of

$x$ and

$y$ is equal to

$180^0$ (By Linear Pair)
A linear pair is a pair of adjacent, supplementary angles. Adjacent means next to each other and supplementary means that the sum of the measures of the two angles is equal to

$180^o$ .

$x = 75^0$

$=> x + y = 180^0$

$=> 75^0 + y = 180^0$

$=> y = 180^0 - 75^0 = 105^0$

$\displaystyle 91^{\circ}$ is an example of

0%
obtuse
0%
acute
0%
right
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Reflex

Explanation

An obtuse angle is one which is more than

$90^0$ but less than

$180^0$ .
and hence

$\displaystyle 91^{\circ}$ is an example of obtuse.

Fill in the blanks with the correct word from the options given.

Parallel lines are ____ intersecting lines.

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Always
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Never
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Sometimes
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Data Insuficient

Explanation

Parallel lines are never intersecting lines.

Option

$B$ is correct.

$\displaystyle 179^{\circ}$ is an example of

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obtuse angle.
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acute angle.
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right angle.
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None of the above

Explanation

An obtuse angle is an angle which is more than

$90^o$ but less than

$180^o$ .
Hence

$\displaystyle 179^{\circ}$ is an example of obtuse.

Hence $Op-A$ is correct.

Which angles in the given figure are complementary?

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$\angle\, 1$ and $\angle\, 2$
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$\angle\, 2$ and $\angle\, 3$
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$\angle\, 3$ and $\angle\, 4$
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$\angle\, 4$ and $\angle\, 1$

Explanation

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

Here,

the sum, $\angle 2+\angle 3$ , is vetrically opposite to a perpendicular.

$\Rightarrow \angle 2+\angle 3={ 90 }^{ \circ }$ .

Hence

$\angle 2$ and

$\angle 3$ are complementary.

Therefore, option

$B$ is correct.

$\displaystyle 89^{\circ}$ is an example of :

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obtuse
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acute
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right
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None of the above

Explanation

Angles between

${0}^{o}$ and

${90}^{o}$ are acute angles. Hence,

${89}^{o}$ is an acute angle.

If two angles in a triangle are

$40^o$ and

$60^o$ , then the third angle is:

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$90^o$
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$80^o$
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$70^o$
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$60^o$

Explanation

Let the third angle be

$x$

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

$180^0$ .

${ 40 }^{ \circ }+{ 60 }^{ \circ }+x={ 180 }^{ \circ }\\ { 100 }^{ \circ }+x={ 180 }^{ \circ }\\ \Rightarrow x={ 80 }^{ \circ }$

Given : AB || CD.

$\angle\, 2$ is an acute angle, then

$\angle\, 1$ is

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Acute
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Right
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Obtuse
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Straight

Explanation

$\angle 1$ and

$\angle 2$ are supplementary angles .

$\Rightarrow \angle 1+\angle 2={ 180 }^{ \circ }$

Now

$\angle 2$ is given acute

$\Rightarrow \angle 2<{ 90 }^{ \circ }$

$\Rightarrow \angle 1>{ 90 }^{ \circ }$

So it is an obtuse angle.

Straight angle is ________

0%
$\displaystyle 90^{\circ}$
0%
$\displaystyle 180^{\circ}$
0%
$\displaystyle 60^{\circ}$
0%
$\displaystyle 45^{\circ}$

Explanation

A straight angle

$= {180}^{o}$

Supplementary angle of

$\displaystyle 102^{\circ}$ is:

0%
$\displaystyle 180^{\circ}$
0%
$\displaystyle 90^{\circ}$
0%
$\displaystyle 78^{\circ}$
0%
$\displaystyle 60^{\circ}$

Explanation

As sum of supplementary angles if

$180^0$

Supplementary angle of

$\displaystyle 102^{\circ}=180^{\circ}-102^{\circ}=78^{\circ}$

Two complementary angles are in the ratio

$1:9$ . The angles are:

0%
$54^\circ,\, 36^\circ$
0%
$9^\circ,\, 81^\circ$
0%
$10^\circ,\, 90^\circ$
0%
$11^\circ,\, 79^\circ$

Explanation

Given, the complementary angles are in the ratio

$1:9$ .

Let the angles be

$x$ and

$9x$ .

We know, sum of the complementary angles is

$90^{ \circ }$ .

$\Rightarrow x+9x={ 90 }^{ \circ }\\ \Rightarrow 10x=9{ 0 }^{ \circ }\\ \Rightarrow x=9^{ \circ }$

Hence, the angles are:

$x=1\times 9^{ \circ }=9^{ \circ }$

and

$9x=9\times 9^{ \circ }=81^{ \circ }$ .

Therefore, option

$B$ is correct.

Find x; if

$\angle\, 1\, =\, 5x\, +\, 15^{\circ}$ and

$\angle\, 2\, =\, 28x$ , angles form linear pair.

0%
$40^{\circ}$
0%
$140^{\circ}$
0%
$5^{\circ}$
0%
$20^{\circ}$

Explanation

$\angle \, 1\, +\, \angle\, 2\, =\, 180^{\circ}$ (Linear pair)

$\Rightarrow\quad 5x\, +\, 15^{\circ}\, +\, 28x\, =\, 180^{\circ}$

$\Rightarrow\quad 33x\, =\, 180^{\circ}\, -\, 15\, =\, 165^{\circ}$

$\Rightarrow\quad x\, =\, \displaystyle \frac {165^{\circ}}{33}\, =\, 5^{\circ}$ .

The supplementary angle of

$120^o$ is:

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$30^o$
0%
$50^o$
0%
$240^o$
0%
$60^o$

Explanation

Let the supplementary angle be

$x$

Sum of supplementary angles is

$180^{\circ}$

$\Rightarrow x+{ 120 }^{ \circ }={ 180 }^{ \circ }\\ \Rightarrow x={ 180 }^{ \circ }-{ 120 }^{ \circ }\\ \Rightarrow x={ 60 }^{ \circ }$

Which two angles are supplementary?

0%
$\angle\, COF$ and $\angle\, AOC$
0%
$\angle\, COF$ and $\angle\, COE$
0%
$\angle\, COF$ and $\angle\, EOD$
0%
$\angle\, COF$ and $\angle\, AOE$

Explanation

$\angle COF$ and

$\angle COE$ are supplementary because they formed on the line

$EOF$

$\Rightarrow \angle COF+\angle COE={ 180 }^{ \circ }$

So option

$B$ is correct.

An angle which is more than

$180^{\circ}$ and less than

$360^{\circ}$ is called:

0%
obtuse angle
0%
right angle
0%
reflex angle
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complete angle

Explanation

By definition, we know, an angle which is more than

$180^o$ 180∘ and less than

$360^o$ 360∘ is called reflex angle.

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

$1$ turn (between

$180^o$ and

$360^o$ ) are called reflex angle.

Therefore, option

$C$ is correct.

Complement angle of the angle is:

0%
$77.4^{\circ}$
0%
$67.3^{\circ}$
0%
$76.3^{\circ}$
0%
$77.3^{\circ}$

Explanation

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

Given, measure of one complementary angle is $12.7^o.$

$\Rightarrow$ Measure of other complementary angle $=90^o-12.7^o$ $=77.3^o.$

$\therefore$ Measure of a complementary angle of $12.7^{o}=77.3^o$ .

An angle which measures

$180^{\circ}$ is called_______angle.

0%
zero
0%
right
0%
straight
0%
acute

Explanation

An angle which measures

${180}^{o}$ is called a straight angle.

A line which intersects two or more lines at different points is:

0%
perpendicular
0%
transversal
0%
parallel
0%
none of these

Explanation

$(A)$ Perpendiculars are the lines which intersect each other.

$(C)$ Parallel lines do not intersect each other at any point.

$(B)$ In geometry, a line that passes through two or more lines in the same plane at two or more different points is called transversal.

Transversals play a role in establishing whether two other lines in the Euclidean plane are parallel.

Hence, option B is correct.

An angle which measures more than

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

$\displaystyle 90^{\circ}$ is called

0%
obtuse
0%
acute
0%
right
0%
none of these

Explanation

Angles which measure more than

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

${90}^{o}$ are acute angles.

CBSE Questions for Class 9 Maths Lines And Angles Quiz 2 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Lines And Angles Quiz 2 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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