MCQ Questions for Class 9 Maths Lines And Angles Quiz 4

What is the measure of supplementary angle of

$32^{\circ}$ ?

0%
$58^{\circ}$
0%
$148^{\circ}$
0%
$138^{\circ}$
0%
$78^{\circ}$

Explanation

Required Measure of supplementary angle

$=180-32$

$=148^0$

If one acute angle of the right angled triangle is half of the other, then the smallest angle is:

0%
$\displaystyle { 90 }^{ o }$
0%
$\displaystyle { 60 }^{ o }$
0%
$\displaystyle { 40 }^{ o }$
0%
$\displaystyle { 30 }^{ o }$

Explanation

Let the acute angle be

$x$ .

Given, the acute angle is half of the other.

Then the other angle is

$2x$ .

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

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

$\implies$

$\displaystyle { 90 }^{ o }+2x+x={ 180 }^{ o }$

$\implies$

$\displaystyle 3x={ 180 }^{ o }-{ 90 }^{ o }$

$\implies$

$\displaystyle x=\frac { { 90 }^{ o } }{ 3 }$

$\implies$

$\displaystyle x={ 30 }^{ o }$ .

Hence, the angles are:

$90^o, x=30^o$ and

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

Here,

$30^o$ is the smallest angle.

Therefore, option

$D$ is correct.

Two angles the sum of whose measure is

$90^{\circ}$ are called ______ angles.

0%
Supplementary
0%
Complementary
0%
Corresponding
0%
None of these

Explanation

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

${ 90^o }$ are called complementary 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.

Therefore, option $B$ is correct.

Which of the following is a straight angle?

0%
Angle that is less that $90^{\circ}$
0%
Angle that is exactly $90^{\circ}$
0%
Angle that is greater than $90^{\circ}$
0%
None of these

Explanation

Straight angle is the angle which is exactly

$180^{\circ}$

Hence option

$D$ is the correct answer.

Find the supplement of the angle

$148^{\circ}$

0%
$32^{\circ}$
0%
$122^{\circ}$
0%
$148^{\circ}$
0%
None of these

Explanation

We know that the supplement angle

$=180^0-\theta$

So,

The supplement angle of

$148^0$ will be

$=180^0-148^0=32^0$

Hence, this is the answer.

In a triangle, the angles are in ratio

$1: 3: 2$ . Find the difference between the greatest and smallest angle of the triangle.

0%
$10^o$
0%
$70^o$
0%
$60^o$
0%
$20^o$

Explanation

Given, the angles are in the ratio

$1:3:2$ .

Let the angles be

$x,3x$ and

$2x$ .

Using angle sum property of triangle,

$x+3x+2x={ 180 }^{ \circ }\\ \Rightarrow 6x={ 180 }^{ \circ }\\ \Rightarrow x={ 30 }^{ \circ }.$

So the angles are :

$x={ 30 }^{ \circ }$ ,

$3x=3\times { 30 }^{ \circ }={ 90 }^{ \circ }$

and

$2x=2\times { 30 }^{ \circ }={ 60 }^{ \circ }$ .

Therefore, the difference between the greatest and the smallest angle

$={ 90 }^{ \circ }-{ 30 }^{ \circ }={ 60 }^{ \circ }$ .

Hence, option

$C$ is correct.

Corresponding angle converse theorem states that :

0%
If two lines and transversal form corresponding angles that are congruent , then the lines are parallel
0%
If two lines and transversal form alternate interior angles that are congruent , then the lines are parallel
0%
If two parallel lines are cut by Transversal then the pair of corresponding angles are congruent
0%
If two lines intersect each other,then the vertically opposite angles are equal

The converse of alternate angle theorem states that :

0%
If two parallel lines are cut by Transversal then the pair of corresponding angles are congruent
0%
If two parallel lines are cut by transversal, then the pair of alternate interior angles are equal
0%
If two lines and a transversal form corresponding angles that are congruent,then the lines are parallel
0%
If two lines intersect each other,then the vertically opposite angles are equal

Which type of angle best describes angle Q?

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

Explanation

Measure of angle

$Q$ is more thaan

$90^o$ but less than

$180^o$ .

Hence the

$\angle Q$ is an obtuse angle.

The supplement of an acute angle is a/an __________ angle.

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

Explanation

We know acute angle

$< 90^{\circ}$

Let us take an example.

$\angle x = 45^{\circ}$ .....

$x$ is an acute angle

Supplement of

$x$ is

$180^{\circ} - 45^{\circ} = 135^{\circ}$ ....it is an Obtuse angle

Obtuse angle

$> 90^{\circ}$ .

The clock shows the time in the morning. Then, angle represents _________ angle.

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

Explanation

Any angle which is larger than

$180^o$ but smaller than

$360^o$ is called as a reflex angle.

Here, the angle shown is larger than

$180^o$ but smaller than

$360^o$ .

Hence, it is a reflex angle.

Therefore, option

$C$ is correct.

An angle which measures more than

$90^o$ but less than

$180^o$ is called ___________.

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

Explanation

An angle which measures more than

$90^o$ but less than

$180^o$ is called as an obtuse angle.

The measure of an angle is four times the measure of its supplementary angle. Then the angles are __________.

0%
$36^o, 144^o$
0%
$40^o, 160^o$
0%
$18^o, 72^o$
0%
$50^o, 200^o$

Explanation

According to the problem,

The measure of an angle which is

$4$ times its supplement.

Supplementary angles means, sum of angles is

$180^o$

Let the measure of one angle be

$x$ , then the measure of its supplementary angle will be

$(180^o-x)$ .

According to the given condition,

$\implies x=4(180^{o}-x)$

$\implies x=4\times 180^{o}-4x$

$\implies 5x=4\times 180^{o}$

$\implies x=4\times 36^{o}=144^{o}$

Hence,

$x=144^{o}$

so these angles are

$36^{\circ}$ ,

$144^{\circ}$

Hence the option

$(A)$ is correct.

In the given measure, measure of

$\angle {b}$ and

$\angle {x}$ are

0%
$\angle x = 90^{\circ}\quad \angle b = 60^{\circ}$
0%
$\angle x = 90^{\circ}\quad \angle b = 30^{\circ}$
0%
$\angle x = 90^{\circ}\quad \angle b = 90^{\circ}$
0%
$\angle x = 90^{\circ}\quad \angle b = 180^{\circ}$

Explanation

${\textbf{Step -1: Use vertically opposite angle properties.}}$

$\angle x$

${\text{is a vertically opposite angle to}}$

$90^0$

${\text{Hence,}}$

$\angle x=90^0$

$\angle b$

${\text{and}}$

$\angle x$

${\text{form a linear pair of angles.}}$

$\Rightarrow 90^0 + \angle b =180^0$

$\Rightarrow \angle b =90^0.$

${\textbf{Hence , the option (C) is correct.}}$

Which one of the following is true for the given triangle?

0%
$\angle 3 = \angle 1 + \angle 2$
0%
$\angle 1 = \angle 3 + \angle 2$
0%
$\angle 2 = \angle 1 + \angle 3$
0%
Both (A) and (B)

Explanation

In 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).

Hence, option

$A$ is correct.

Find the supplement of

$98^o$ :

0%
${82^ \circ }$
0%
${124^ \circ }$
0%
${122^ \circ }{45^\iota }$
0%
${135^ \circ }{20^\iota }{26^{\iota \iota }}$

Explanation

The supplement of

${98}^{\circ}$ is the angle that when added to

${98}^{\circ}$ forms a straight angle

${180}^{\circ}$

To determine the supplement, subtract the given angle from

${180}^{\circ}$ .

${180}^{\circ}-{98}^{\circ}={82}^{\circ}$

The supplement of

${98}^{\circ}$ is

${82}^{\circ}$

____ pairs of corresponding angles formed by a transversal of two parallel lines.

0%
Two
0%
Three
0%
Four
0%
Eight

Explanation

We know that

$Four$ pairs of corresponding angles formed by a transversal of two parallel lines.

1238375_1292328_ans_05e38e1a9d7d4e908f43588cbe8b5b54.png

State true (T) or false (F)

Lines that meet at a common point are called parallel lines.

0%
True
0%
False

Say True or False.
The measure of an obtuse angle

$< 90^{\circ}$ .

0%
True
0%
False

Explanation

False

The measure of an obtuse angle is greater than

$90^o$ but less than

$180^o$ .

State True or False:
The measure of a reflex angle is

$> 180^{\circ}$ .

0%
True
0%
False

Explanation

Step 1: True

According to definition, reflex angle is the angle which are greater than

$180^o$ but less than

$360^o$ . Therefore, the given statement is true.

An angle whose measure is less than that of a right angle is ______.

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

Explanation

$Acute \ angle$ has measure less than

$right \ angle$

Hence correct answer is

$A) \ Acute$

An angle whose measure is greater than that of a right angle is ______.

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

Explanation

$Obtuse \ angle$ has measure more than that of

$right \ angle \ but \ less \ than \ 180\ degree$

Hence correct answer is

$B) \ Obtuse$

An angle whose measure is the sum of the measures of two right angles is _______.

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

Explanation

Step 1: Straight angle

We know that the measure of a right angle is

$90^ \circ$ and the measure of a straight angle is

$180^ \circ.$

Therefore, sum of the measure of two right angles is

$(90+90)^ \circ=180^ \circ.$

Thus an angle whose measure is the sum of two right angles is

$\text{Straight}.$

Is the following statement true (T) and which are false (F)?
All the angles of a triangle can be equal to

$60^{\circ}$ .

0%
True
0%
False

Explanation

Given all the angles are equal to

$60^o$ .

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

$180^o$ .

Then,

$60^o+60^o+60^o=120^o+60^o=180^o$ .

Hence, it is possible for all the angles of a triangle to be equal to

$60^o$ .

That is, the statement is true and option

$A$ is correct.

Choose the correct option.

$60^{\circ}$ is

0%
Acute angle
0%
Obtuse angle
0%
Reflex angle
0%
none of these

Choose the correct option.

$20^{\circ}$ is

0%
Acute angle
0%
Obtuse angle
0%
Reflex angle
0%
None of these

Choose the correct option:-

$200^{\circ}$ is ________.

0%
Acute $\angle$
0%
Obtuse $\angle$
0%
Reflex $\angle$
0%
none of these

Explanation

The given measure of angle is

$200^o.$

We know, reflex angles are angles measuring greater than

$180^o$ and less than

$360^o.$

$\therefore$

$200^o$ is a reflex angle.

Hence, option

$C$ is correct.

Open any two adjacent fingers of your hand. What kind of angle you get

0%
acute
0%
right
0%
obtuse
0%
straight

State whether the following statement are true or false :
'An angle Whose measure is greater than that of right angle is obtuse'.

0%
True
0%
False

If the sum of two angles is an obtuse angle, then which of the following is not possible :

0%
two acute angles
0%
one obtuse angles one acute angle
0%
two acute angles
0%
two right angles

CBSE Questions for Class 9 Maths Lines And Angles Quiz 4 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Lines And Angles Quiz 4 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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