Tag: complementary angle, supplementary angles and adjcent angles

Quizzes (7) Questions (38)

Questions Related to complementary angle, supplementary angles and adjcent angles

Multiple choice maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

Find the angles in each of the following.
Two complementary angles are in the ratio $3 : 2$

  1. $54^{\circ}, 36^{\circ}$
  2. $44^{\circ}, 36^{\circ}$
  3. $54^{\circ}, 46^{\circ}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the angles be $3x$ and $2x$.


So,
$3x+2x=90^0$

$5x=90^0$

$x=18^0$

Therefore, the angle are
$54^0, 36^0$


Hence, this is the answer.

Multiple choice maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

If $\angle A$ is complement to $30^o$ and $\angle B $ is supplement to $120^o$ then:

  1. $\angle A > \angle B$
  2. $\angle A < \angle B$

  3. Incomparable
  4. $\angle A = \angle B$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sum of complementary angles is $90^{\circ}$

$\Rightarrow \angle A+{ 30 }^{ \circ  }={ 90 }^{ \circ  }\ \Rightarrow \angle A={ 60 }^{ \circ  }$
Sum of supplementary angles is $180^{\circ}$
$\Rightarrow \angle B+{ 120 }^{ \circ  }={ 180 }^{ \circ  }\ \Rightarrow \angle B={ 60 }^{ \circ  }$
$\Rightarrow \angle A=\angle B$

Multiple choice maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

Which is the greatest angle in the given set: $\dfrac{1}{3}$ of complete angle, $\dfrac{1}{3}$ of straight angle or a right angle?

  1. $\dfrac{1}{3}$ of complete angle
  2. $\dfrac{1}{3}$ of straight angle

  3. A right angle

  4. All are equal
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Complete angle $=360^{\circ}$

$\dfrac{1}{3}$ complete angle $=\dfrac { 1 }{ 3 } \times { 360 }^{ \circ  }={ 120 }^{ \circ  }$
Right angle $=90^{\circ}$
$\dfrac{1}{3}$ right angle $=\dfrac { 1 }{ 3 } \times { 90 }^{ \circ  }={ 30 }^{ \circ  }$
So $\dfrac{1}{3}$ complete angle is greater.

Multiple choice maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

Rank the following angles in descending order. 
1. Straight angle
2. Reflex angle
3. Right angle 

  1. $2$, $1$, $3$
  2. $3$, $2$, $1$
  3. $2$, $3$, $1$
  4. $3$, $1$, $2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
  1. Right angle $=90^{\circ}$

    2. Straight angle $=180^{\circ}$

    3. Reflex angle lies between $180^{\circ}$ and $360^{\circ}$

    So the descending order of angles is
    $2>1>3$
Multiple choice maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

In a triangle, the angles are in ratio $1: 3: 2$. Find the difference between the greatest and smallest angle of the triangle.

  1. $10^o$
  2. $70^o$
  3. $60^o$
  4. $20^o$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Le the angles be $x,3x$ and $2x$

Using angle sum property of triangle 
$x+3x+2x={ 180 }^{ \circ  }\ 6x={ 180 }^{ \circ  }\ \Rightarrow x={ 30 }^{ \circ  }$
So the angles are 
$x={ 30 }^{ \circ  }\ 3x=3\times { 30 }^{ \circ  }={ 90 }^{ \circ  }\ 2x=2\times { 30 }^{ \circ  }={ 60 }^{ \circ  }$
Difference between largest and smallest $={ 90 }^{ \circ  }-{ 30 }^{ \circ  }={ 60 }^{ \circ  }$

Multiple choice maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

If the difference of two supplementary angles is $40^{\circ}$, then the measurement of the greater angle is

  1. $65^{\circ}$
  2. $110^{\circ}$
  3. $130^{\circ}$
  4. $220^{\circ}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the two supplementary angles are $x^{\circ}$ and
$180^{\circ} - x$
By hypothesis, $x - (180^{\circ} - x) = 40^{\circ}$
or $2x - 180^{\circ} = 40^{\circ}$
or  $2x = 220^{\circ}$
or    $x = 110^{\circ}$

Multiple choice maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

In a $\Delta$ PQR, if $3\sin P+4\cos Q=6$ and $4 \sin Q+3\cos P=1$, then the angle $R$ is equal to :

  1. $\dfrac{3\pi}{4}$
  2. $\dfrac{5\pi}{6}$
  3. $\dfrac{\pi}{6}$
  4. $\dfrac{\pi}{4}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given trignometric equations are:

$3 \sin{P} +4 \cos{Q} =6$ -------(1)
$4 \sin{Q} +3 \cos{P} =1$ -------(2)

Squaring both equations (1) and (2) and adding them, we get
$\Rightarrow 9\left( \sin ^{ 2 }{ P } +\cos ^{ 2 }{ P }  \right) +16\left( \sin ^{ 2 }{ Q } +\cos ^{ 2 }{ Q }  \right) +24\left( \sin { Q } \cos { P } +\cos { Q } \sin { P }  \right) =36+1$

$ \Rightarrow 9+16+24\sin { \left( P+Q \right)  } =37$

$ \therefore \sin { \left( P+Q \right)  } =\cfrac { 37-25 }{ 24 } =\cfrac { 12 }{ 24 } =\cfrac { 1 }{ 2 } $

$\therefore P+Q=30°$

Hence, angle $R=180°-30°=150°=\cfrac { 5\pi  }{ 6 } $radian

Multiple choice maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

In triangle $ABC,$ if $\dfrac { 1 }{ a+c } +\dfrac { 1 }{ b+c } =\dfrac { 3 }{ a+b+c } ,$ then $\angle c$  is equal to:

  1. $30^{\circ}$
  2. $45^{\circ}$
  3. $60^{\circ}$
  4. $90^{\circ}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given: $\cfrac { 1 }{ a+c } +\cfrac { 1 }{ b+c } =\cfrac { 3 }{ a+b+c } $


$\Rightarrow \quad \cfrac { a+b+2c }{ (a+c)(b+c) } =\cfrac { 3 }{ a+b+c } $

$ \therefore (a+b+2c)(a+b+c)=3(a+c)(b+c)$

$\Rightarrow$ $ { a }^{ 2 }+ab+ac+ab+{ b }^{ 2 }+bc+2ac+2bc+2{ c }^{ 2 }$$ =3(ab+ac+bc+{ c }^{ 2 })$

$ \therefore { a }^{ 2 }+2ab+3ac+{ b }^{ 2 }+3bc+2{ c }^{ 2 }$$ =3ab+3ac+3bc+3{ c }^{ 2 }$

$\Rightarrow$ ${ a }^{ 2 }+{ b }^{ 2 }=ab+{ c }^{ 2 }$

$\Rightarrow$ $ { a }^{ 2 }+{ b }^{ 2 }-{ c }^{ 2 }=ab$

$\Rightarrow$ $ \cfrac { { a }^{ 2 }+{ b }^{ 2 }-{ c }^{ 2 } }{ ab } =1$

$\Rightarrow \cfrac { { a }^{ 2 }+{ b }^{ 2 }-{ c }^{ 2 } }{ 2ab } =\cfrac { 1 }{ 2 } $

$\cos { C } =\dfrac{1}{2}\Rightarrow \angle C={ 60 }^{\circ}$

Multiple choice maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

In $\Delta ABC\,,\,if\,\,A\,\,:\,\,B\,:\,\,C\, = \,1\,\,:\,\,5\,\,:\,\,6\,\,then$ find the value of $\sin A: \sin B: \sin C$

  1. $\left( {\sqrt 3 \, - \,1} \right)\,:\,2\sqrt 2 \,:\,\left( {\sqrt 3 \, + \,1} \right)$
  2. $2\sqrt 2 \,:\,\left( {\sqrt 3 \, - \,1} \right)\,:\,\left( {\sqrt 3 \, + \,1} \right)$
  3. $ \,\left( {\sqrt 3 \, - \,1} \right)\,:\,\left( {\sqrt 3 \, + \,1} \right)\,:\,2\sqrt 2 $
  4. $ \,\left( {\sqrt 3 \, - \,1} \right)\,:\,\sqrt 3 :\,\sqrt 2 $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given that $ A:B:C = 1:5:6 $


We know that the sum of angles in a triangle is $180^0$

Let us first find each angle.

Total no.of parts= $1+5+6= 12$

$A$= $ \dfrac{1}{12} $ ($180^0$) =$15^0$

$B$= $ \dfrac{5}{12} $ ($180^0$) =$75^0$

$C$= $ \dfrac{6}{12} $ ($180^0$) =$90^0$

Hence, $ \sin A: \sin B: \sin C$ = $\sin 15^o$$:\sin 75^o$$:\sin 90^o$

$=\dfrac {\sqrt{3}-1} {2\sqrt 2} : \ \dfrac{\sqrt3+1}{2\sqrt2 } :1$ 

$= ({\sqrt{3}-1})  : ({\sqrt3+1} ): ({2\sqrt2 }) $