Tag: types of angle

Questions Related to types of angle

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

maths construction of angles identifying angles acute and obtuse angles types of angle

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

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

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

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

  5. none of these

Show answer
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:

maths construction of angles identifying angles acute and obtuse angles types of angle

  1. Reflex angle

  2. Straight angle

  3. Obtuse angle

  4. Acute angle

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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:

maths construction of angles identifying angles acute and obtuse angles types of angle

  1. Obtuse angle

  2. Right angle

  3. Acute angle

  4. Reflex angle

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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:

maths construction of angles identifying angles acute and obtuse angles types of angle

  1. Acute angles

  2. Obtuse angles

  3. Right angles

  4. All of the above

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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?

maths construction of angles identifying angles acute and obtuse angles types of angle

  1. Two right angles

  2. One and half right angles

  3. One right angle

  4. Half a right angle

Show answer
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:

maths construction of angles identifying angles acute and obtuse angles types of angle

  1. $[0˚, 90˚)$

  2. $(0˚, 90˚]$

  3. $[90˚, 180˚)$

  4. $(90˚, 180˚)$

Show answer
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?

maths construction of angles identifying angles acute and obtuse angles types of angle

  1. $12 : 00$

  2. $12 : 30$

  3. $8 : 43$

  4. $8 : 00$

Show answer
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 ___________.

maths construction of angles identifying angles acute and obtuse angles types of angle

  1. Acute

  2. Obtuse

  3. Right

  4. None of these

Show answer
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 $< 90^{o}$

maths construction of angles identifying angles acute and obtuse angles types of angle

  1. True

  2. False

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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?

maths construction of angles identifying angles acute and obtuse angles types of angle

  1. An acute angle

  2. An obtuse angle

  3. A straight angle

  4. A complete angle

Show answer
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.