Tag: angle and its measurement

Questions Related to angle and its measurement

In $\displaystyle \angle PRQ $, the two arms are:

mathematics and statistics angle and its measurement directed angles

  1. $\displaystyle \overrightarrow{PR} $ and $\displaystyle \overrightarrow{RQ} $

  2. $\displaystyle \overrightarrow{RP} $ and  $\displaystyle \overrightarrow{PQ} $

  3. $\displaystyle \overrightarrow{QR} $ and $\displaystyle \overrightarrow{QP} $

  4. None of the above

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Correct Option: A
Explanation:
An angle is made by the intersection of two lines and that lines are also called as arms.
In $\angle{PRO}$, the angle is formed by the intersection of $\overrightarrow{PR}$ and $\overrightarrow{RO}$ at $R$.
Hence, the two arms are $\displaystyle \overrightarrow{PR} $ and $\displaystyle \overrightarrow{RQ} $.

To draw an angle of $150^o$ using a pair of compass and ruler ______.

mathematics and statistics angle and its measurement directed angles

  1. Bisect angle between $120^o$ and $180^o$

  2. Bisect angle between $60^o$ and $120^o$

  3. Bisect angle between $0^o$ and $160^o$

  4. None of these

Show answer
Correct Option: A
Explanation:

To draw an angle of 150° using a pair of compass and 

rule we bisect an angle between 120° and 180° 
$\rightarrow$ Since 120°<150°<180° we bisect angle
     between 120° and 180°

If the sum of two angles is equal to an obtuse angle, then which of the following is NOT possible?

mathematics and statistics angle and its measurement directed angles

  1. One obtuse and one acute angle

  2. One right angle and one acute angle

  3. Two acute angles

  4. Two right angles

Show answer
Correct Option: D
Explanation:

Obtuse angles are those angles whose measure is more than$90°$ but less than $180°$.


Since, sum of two right angles is $90°+90°=180°$.

Hence sum of two right angles can not be an obtuse angle.

Choose the correct answers from the alternatives given.
In $\Delta $ABC, the sides AB and AC are produced to P and Q respectively. The bisectors of $\angle PBC  \, and \,  \angle QCB $ intersect at a point 0. then $\angle BOC$ is equal to:

mathematics and statistics angle and its measurement directed angles

  1. 90- $\frac{1}{2} \angle A$

  2. 90+ $\frac{1}{2} \angle A$

  3. $120^{\circ}$ + $\frac{1}{2} \angle A$

  4. 120 - $\frac{1}{2} \angle A$

Show answer
Correct Option: A
Explanation:

2 $\angle 1 + \angle B = 180^{circ}$         (linear pair)
$\angle 1 = 90^{\circ}-\dfrac{1}{2}\angle B$          (1)
Similarly,
$\angle 2 = 90^{\circ} - \dfrac{1}{2} \angle C$   (2)
$\angle BOC = 180^{circ}-  (\angle 1 + \angle 2)$
=$180^{circ}- [180^{circ}-\dfrac{1}{2}$ ($\angle B + \angle C$)]
=$\dfrac{1}{2}[\angle B + \angle C] = \dfrac{1}{2} (180^{circ} - \angle A) = 90^{circ}-\dfrac{1}{2} \angle A$

A half turn about O is a rotation through angel of ____ or ____

mathematics and statistics angle and its measurement directed angles

  1. $-90^0, +90^0$

  2. $+180^0, -180^0$

  3. $+360^0, -360^0$

  4. $-270^0, +270^0$

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Correct Option: B

Convert $40^\circ \,20'$ into radian measure.

mathematics and statistics angle and its measurement degree measure of angle measure of angle radians or degrees

  1. $\dfrac {121}{540}\pi $ radians

  2. $\dfrac {121}{570}\pi $ radians

  3. $\dfrac {120}{513}\pi $ radians

  4. None

Show answer
Correct Option: A
Explanation:
Given: ${40^0}$${{{20}^{'}}}$

${40^0} + \dfrac{{{{20}^0}}}{{{{60}^0}}}  $

$=40 + \dfrac{1^o}{3} = \dfrac{{{{121}^0}}}{3}$

$radian = \dfrac{\pi }{{180^o}} \times \dfrac{{121^o}}{3}$

$\boxed{ = \dfrac{{121}}{{540}}\pi \;radians}$