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Multiple choice maths construction of angles identifying angles acute and obtuse angles types of 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
Reveal answer Fill a bubble to check yourself
A Correct answer
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
$=\theta _2-\theta _1$
$=75.96-71.56$
$=4.4^{0}$

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

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

  1. Reflex angle

  2. Straight angle

  3. Obtuse angle

  4. Acute angle
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $\displaystyle {360 }^{ o }$.

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

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
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $\displaystyle {360 }^{ o }$.

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

The sum of two acute angles can be:

  1. Acute angles

  2. Obtuse angles

  3. Right angles

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

Multiple choice maths construction of angles identifying angles acute and obtuse angles types of 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
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

Range of an obtuse angle is:

  1. $[0˚, 90˚)$
  2. $(0˚, 90˚]$
  3. $[90˚, 180˚)$
  4. $(90˚, 180˚)$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $\displaystyle {360 }^{ o }$.