Tag: measurement of an angle

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Questions Related to measurement of an angle

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

In a $\displaystyle \Delta PQR$ PQ = PR and $\displaystyle \angle Q$ is twice that of $\displaystyle \angle P$ Then $\displaystyle \angle Q$__

  1. 75$\displaystyle ^{\circ}$
  2. 65$\displaystyle ^{\circ}$
  3. 72$\displaystyle ^{\circ}$
  4. 100$\displaystyle ^{\circ}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\displaystyle \because $ PQ = PR 
$\displaystyle \Rightarrow $ $\displaystyle \angle Q=\angle R$
Given that $\displaystyle \angle Q=2\angle P$
We have
$\displaystyle \angle P+\angle Q+\angle R=180^{\circ}$
$\displaystyle \frac{\angle Q}{2}+\angle Q+\angle Q=180^{\circ}$
$\displaystyle \frac{5}{2}\angle Q=180^{\circ}$
$\displaystyle \angle Q=72^{\circ}$        

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

Find the angle between the lines 3x + 2y = 6 and x + y = 6

  1. 12$\displaystyle ^{\circ}$ 20'
  2. 11$\displaystyle ^{\circ}$ 19'
  3. 14$\displaystyle ^{\circ}$ 25'
  4. 13$\displaystyle ^{\circ}$ 06'
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Line  $3x+2y=6$

$=>2y=-3x+6$
$=>y=\frac{-3}{2}x+\frac{6}{2}$
$=>m'=\frac{-3}{2}x$
$\therefore tan\theta _1=\frac{-3}{2}$
$=>\theta _1=tan^{-1}(\frac{-3}{2})$
$=>\theta _1=-56.31$
Line is $x+y=6$
$=>y=x+6$
$=>m _2=-1$
$=>tan\theta _2=-1$
$=>\theta _2=tan^{-1}(-1)$
$=>\theta _2=-45$
Thus, ale between them $=(-45-56.31)$
                                          $=11.31^0$

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.
The angle whose complement is one sixth of its supplement

  1. $72^{\circ}$
  2. $32^{\circ}$
  3. $62^{\circ}$

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

Let the angle be $x^0$.


Supplement angle $=(180^0-x)$

Complement angle $=(90^0-x)$

According to the question,
$\dfrac{1}{6}\times (180^0-x)=(90^0-x)$

$(180^0-x)=6(90^0-x)$

$180^0-x=540^0-6x$

$5x=360^0$

$x=72^0$


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

Find the angles in each of the following.
The angle which is four times its supplement

  1. $144^{\circ}$
  2. $44^{\circ}$
  3. $14^{\circ}$

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

Let the angle be $x^0$.


According to the question,
Supplement angle $=(180^0-x)\times 4$

So,

$x=720^0-4x$

$5x=720^0$

$x=144^0$


Hence, this is the answer.