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Identifying angles - class-VI

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Say True or False.
The measure of an obtuse angle $< 90^o$.

  1. True

  2. False


Correct Option: B
Explanation:

False
The measure of an obtuse angle is greater than $90^o$ but less than $180^o$.

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

  1. Acute

  2. Obtuse

  3. Right

  4. Straight


Correct Option: D
Explanation:

Measure of a right angle is $90^ \circ$

Measure of a straight angle is $180^ \circ$
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 $Straight$

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

  1. Acute

  2. Obtuse

  3. Right

  4. Straight


Correct Option: B
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 less than that of a right angle is ______.

  1. Acute

  2. Obtuse

  3. Right

  4. Straight


Correct Option: A
Explanation:

$Acute \ angle$ has measure less than $right \ angle$

Hence correct answer is $A) \ Acute$

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

  1. obtuse

  2. acute

  3. right

  4. None of the above


Correct Option: B
Explanation:

Angles between $ {0}^{o} $ and $ {90}^{o} $ are acute angles. Hence, $ {89}^{o} $ is an acute angle.

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

  1. $35^\circ,\, 69^\circ,\, 76^\circ$

  2. $60^\circ,\, 60^\circ,\, 60^\circ$

  3. $88^\circ,\, 46^\circ,\, 46^\circ$

  4. $90^\circ,\, 45^\circ,\, 45^\circ$


Correct Option: D
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.

An angle which measures more than $0^{\circ}$ and less than $90^{\circ}$ is called.

  1. Obtuse

  2. Acute

  3. Right

  4. None


Correct Option: B
Explanation:

Angles which measure $ {0}^{o} $ and less than $ {90}^{o} $ are acute angles.



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

  1. obtuse

  2. acute

  3. right

  4. none


Correct Option: A
Explanation:

Angles between $ {90}^{o} $ and $ {180}^{o} $ are obtuse angles.

Hence, $ {179}^{o} $ is an obtuse angle.

An angle which measures $180^{\circ}$ is called_______angle.

  1. zero

  2. right

  3. straight

  4. acute


Correct Option: C
Explanation:

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

An angle which measures $180^o$ is called a

  1. straight angle

  2. obtuse angle

  3. right angle

  4. complete angle


Correct Option: A
Explanation:

An angle which measures $180^o$ is called a straight angle

The number of acute angles in a triangle is 

  1. At least $1$ and utmost $2$

  2. At least $2$

  3. Exactly $2$

  4. Exactly $3$


Correct Option: B
Explanation:

An acute triangle has three acute angles (utmost). An obtuse (or right) triangle has two acute angles. A triangle has at least two acute angles.

$\displaystyle 80^{0}$ is an example of-

  1. Acute

  2. Obtuse

  3. Right

  4. None of these


Correct Option: A
Explanation:

angles greater than 0 degree and less than 90 degrees are known as acute angles..

hence 80 degrees is an example of acute angle..

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

  1. Acute

  2. Obtuse

  3. Right

  4. None of these


Correct Option: B
Explanation:

obtuse angles are those angles which are greater than 90 degrees and less than 180 degrees..

so,96 degrees is an example of obtuse angle.. 

An angle which measures $\displaystyle 180^{0}$ is called-

  1. Acute

  2. Right

  3. Zero

  4. None of these


Correct Option: D
Explanation:

an angle which measures 180 degrees is calles straight angle..

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

  1. Acute

  2. Right

  3. Obtuse

  4. None of these


Correct Option: C
Explanation:

angles greater than 90 degrees and less than 180 degrees are known as obtuse angles..

hence 170 degrees is an example of obtuse angle..

An angle which measures more than $\displaystyle 0^{0}$ and less than $\displaystyle 90^{0}$ is called-

  1. Obtuse

  2. Right

  3. Acute

  4. None of these


Correct Option: C
Explanation:

an angle which measures more than 0 degree and less than 90 degree is called an acute angle..

What is the acute angle between the lines y = 3x + 2 and y = 4x + 9?

  1. 4.4$\displaystyle ^{\circ}$

  2. 28.3$\displaystyle ^{\circ}$

  3. 5.2$\displaystyle ^{\circ}$

  4. 18.6$\displaystyle ^{\circ}$

  5. none of these


Correct Option: A
Explanation:

$y=3x+2$

$m _1=3$
$=>tan\theta _1=3$
$=>\theta _1=tan^{-1}(3)$
$=>\theta _1=71.57^{0}$
Again,
$y=4x+9$
$=>m _2=4$
$=>tan\theta _2=4$
$=>\theta _2=tan^{1}(4)$
$=>\theta _2=75.96^{0}$
$\therefore$ Angle between the lines
$=\theta _2-\theta _1$
$=75.96-71.56$
$=4.4^{0}$

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

  1. Reflex angle

  2. Straight angle

  3. Obtuse angle

  4. Acute angle


Correct Option: D
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 $\displaystyle {360 }^{ o }$.

If the angle is greater than $\displaystyle { 0 }^{ o }$ and less than $\displaystyle { 90 }^{ o }$, then the angle is known as:

  1. Obtuse angle

  2. Right angle

  3. Acute angle

  4. Reflex angle


Correct Option: C
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 $\displaystyle {360 }^{ o }$.

The sum of two acute angles can be:

  1. Acute angles

  2. Obtuse angles

  3. Right angles

  4. All of the above


Correct Option: D
Explanation:

Let one angle is $\displaystyle { 30 }^{ o }$ and the other angle is $\displaystyle { 40 }^{ o }$ then sum $\displaystyle { 70 }^{ o }$. which is an acute angle.
Let one angle be $\displaystyle { 70 }^{ o }$ and other angle is $\displaystyle { 80 }^{ o }$, then sum is $\displaystyle { 150 }^{ o }$ which is obtuse angle.
Let one angle is $\displaystyle { 45 }^{ o }$ and another angle is $\displaystyle { 45 }^{ o }$ then sum is $\displaystyle { 90 }^{ o }$ which is right angle.

Which of the following is obtuse angle?

  1. Two right angles

  2. One and half right angles

  3. One right angle

  4. Half a right angle


Correct Option: B
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.

Range of an obtuse angle is:

  1. $[0˚, 90˚)$

  2. $(0˚, 90˚]$

  3. $[90˚, 180˚)$

  4. $(90˚, 180˚)$


Correct Option: D
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 $\displaystyle {360 }^{ o }$.

At which one of the following times is the angle between the hands of the clock equal to one straight angle?

  1. $12 : 00$

  2. $12 : 30$

  3. $8 : 43$

  4. $8 : 00$


Correct Option: B
Explanation:

A straight angle can be formed when the hour and minute hands becomes $180^0$ and that happens at $12:30$

An angle which measures more than $90^o$ but less than $180^o$ is called ___________.

  1. Acute

  2. Obtuse

  3. Right

  4. None of these


Correct Option: B
Explanation:

An angle which measures more than $90^o$ but less than $180^o$ is called as an obtuse angle.

The measure of an acute angle is always $< 90^{o}$

  1. True

  2. False


Correct Option: A
Explanation:

Acute angles are angles whose measurements fall between 0 and 90 degrees.

 $\therefore$ The above statement is true.

Mark the correct alternative of the following.
An angle of measure $140^o$ is?

  1. An acute angle

  2. An obtuse angle

  3. A straight angle

  4. A complete angle


Correct Option: B
Explanation:

An angle that measures $<180^o$ but $>90^o$ is called an obtuse angle.

Here it is given $140^o$, so it is an obtuse angle.

Mark the correct alternative of the following.
An angle of measure $180^o$ is called?

  1. A zero angle

  2. A right angle

  3. A straight angle

  4. A reflex angle


Correct Option: C
Explanation:

An angle of measure $180^o$ is called a straight  angle. [ Using definition of the straight angle]

Angle formed by straight angle is _____ .

  1. $90^{\circ}$

  2. $180^{\circ}$

  3. $60^{\circ}$

  4. $45^{\circ}$


Correct Option: B
Explanation:

Angle formed by straight angle $=180^o$

Measure of an obtuse angle is

  1. $>\, 0^{\circ},\, <\, 90^{\circ}$

  2. $>\, 90^{\circ},\, <\, 180^{\circ}$

  3. $>\, 0^{\circ},\, <\, 270^{\circ}$

  4. $>\, 0^{\circ},\, <\, 180^{\circ}$


Correct Option: B
Explanation:

Measure of obtuse angle

$90^o<x<180^o [>90^o, < 180^o]$

An angle which measures more than $\displaystyle 0^{o}$ and less than $\displaystyle 90^{o}$ is called:

  1. obtuse

  2. acute

  3. right

  4. none


Correct Option: B
Explanation:

An angle which measure more than $0^o$ and less than $90^o$ is an acute angle.

An angle which measure more than $90^o$ and less than $180^o$ is an obtuse angle.
Hence, the answer is acute.

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

  1. obtuse angle

  2. acute angle

  3. right angle

  4. None of the above


Correct Option: B
Explanation:
An angle with measure $=90^{o}$ is a right angle
An angle with measure $>90^{o}$ is an obtuse angle
An angle with measure $<90^{o}$ is an acute angle

Here, $89^o$ is less than $90^o$. 

Hence, it is an acute angle.

Straight angle measures _____.

  1. $\displaystyle 90^{o} $

  2. $\displaystyle 180^{o} $

  3. $\displaystyle 60^{o} $

  4. $\displaystyle 45^{o} $


Correct Option: B
Explanation:

An straight angle always makes an angle of $ 180^o $.

Hence, the answer is $180^{o}$.

$\displaystyle 179^{o}$ is an example of:

  1. obtuse angle 

  2. acute angle

  3. right angle

  4. None of the above


Correct Option: A
Explanation:
An angle with measure $=90^{o}$ is a right angle
An angle with measure $>90^{o}$ is an obtuse angle
An angle with measure $<90^{o}$ is an acute angle

Here, $179^o$ is greater than $90^o$ and less than $180^{o}$. 

Hence, it is an obtuse angle.

An angle which measures $\displaystyle 180^{o}$ is called:

  1. zero angle

  2. right angle

  3. straight angle

  4. acute angle


Correct Option: C
Explanation:

An angle which measure $0^0$ is called zero angle.

An angle which measure more than $0^o$ and less than $90^o$ is an acute angle.
An angle which measures $90^o$ is called a right angle.

An angle which measure more than $90^o$ and less than $180^o$ is an obtuse angle.
An straight line makes the angle of $180^o$.
Hence, the answer is straight angle.

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