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Angles and their measurement · Rajasthan Board (RBSE) STD 6 (Rajasthan - English Medium). 42 questions.

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Question 11 Mark
Construct the following angles with help of a protractor: $165^\circ $
Answer


Draw a ray $OP$.
Place the protractor in such a way that its centre lies exactly at $O$ and the base line lies along $OP.$
Starting from $0^\circ $ on the side of $P,$ look for the $165^\circ $ mark on the protractor.
Mark a point $Q$ at this $165^\circ $ mark. Remove the protractor and draw the ray $OQ.$
Then, $\angle\text{POQ}$ is the required angle whose measure is $165^\circ $.
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Question 21 Mark
Measure of the following angles with the help of a protractor and write the measure in degrees:
Answer
The given angle is $\angle\text{PQR}.$ Place the protractor in such a way that its centre is exactly on the vertex $Q$ of the given angle and the base line lies along the arm $QR$. Read of the mark through which the arm $QP$ passes, starting from $0^\circ $ on the side of $R$.

We find that $\angle\text{PQR}=67^\circ.$
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Question 31 Mark
State the type of the following angles:
Answer
$\angle\text{AOB}$ is an obtuse angle since its measure is more than $90^\circ .$
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Question 41 Mark
State the type of the following angles:
Answer
$\angle\text{HOG}$ is an acute angle since its measure is more than $0$ but less than $90^\circ .$
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Question 51 Mark
See the adjacent figure and state the following statement are true and false.

Point $B$ is in the exterior of $\angle\text{AOD}.$
Answer
True.
Point $B$ lies in the exterior of angle $AOD.$
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Question 61 Mark
How many angles are formed in the figures given below? Name them.
Answer
In the given figure, eight angles are formed.
$\angle\text{ABC},\angle\text{BCD},\angle\text{CDA},\angle\text{BAD},\angle\text{ABD},\angle\text{DCB},\angle\text{ADB and }\angle\text{BDC}$
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Question 71 Mark
Classify the angles whose magnitudes are given below: $179^\circ $
Answer
Obtuse angle. This is because its measure is more than $90^\circ $ but less than $180^\circ $
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Question 81 Mark
Classify the angles whose magnitudes are given below: $91^\circ $
Answer
Obtuse angle. This is because its measure is more than $90^\circ $ but less than $180^\circ $
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Question 91 Mark
Measure of the following angles with the help of a protractor and write the measure in degrees:
Answer
The given angle is $\angle\text{LMN}.$ Place the protractor in such a way that its centre is exactly on the vertex $M$ of the given angle and the base line lies along the arm $ML$. Read off the mark through which the arm $MN$ passes, starting from $0^\circ $ on the side of $L$.

We find that $\angle\text{LMN}=50^\circ.$
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Question 101 Mark
Classify the angles whose magnitudes are given below: $80^\circ $
Answer
Acute angle. This is because its measure is more than $0^\circ $ but less than $90^\circ $
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Question 111 Mark
Measure of the following angles with the help of a protractor and write the measure in degrees:
Answer
The given angle is $\angle\text{DEF}.$ Place the protractor in such a way that its centre is exactly on the vertex $E$ of the given angle and the base line lies along the arm $ED$. Read off the mark through which the arm $EF$ passes, starting from $0^\circ $ on the side of $D$.

We find that $\angle\text{DEF}=130^\circ.$
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Question 121 Mark
Measure of the following angles with the help of a protractor and write the measure in degrees:
Answer
The given angle is $\angle\text{RST}.$ Place the protractor in such a way that its centre is exactly on the vertex $S$ of the given angle and the base line lies along the arm $SR$. Read off the mark through which the arm $ST$ passes, starting from $0^\circ $ on the side of $R$.

We find that the $\angle\text{RST}=130^\circ.$
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Question 131 Mark
State the type of the following angles:
Answer
$\angle\text{POP}$ is a complete angle since its measure is $360^\circ .$
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Question 151 Mark
How many degrees are there in the angle between the hour hand and the minute hand of a clock, when it is: $9 o'$ clock?
Answer
$90^\circ .$
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Question 161 Mark
How many angles are formed in the figures given below? Name them.
Answer
In the given figure, three angles are formed.
Names of the angles are: $\angle\text{ABC},\angle\text{BAC and }\angle\text{ACB}$
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Question 171 Mark
How many degrees are there in the angle between the hour hand and the minute hand of a clock, when it is: $3$ o'clock?
Answer
$90^\circ $.
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Question 181 Mark
Classify the angles whose magnitudes are given below: $128^\circ $
Answer
Obtuse angle. This is because its measure is more than $90^\circ $ but less than $180^\circ $
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Question 191 Mark
See the adjacent figure and state the following statement are true and false.

Point $D$ is the interior of $\angle\text{AOC}.$
Answer
False.
Point $D$ lies in the exterior of angle $AOC.$
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Question 201 Mark
See the adjacent figure and state the following statement are true and false.

Ponit $C$ is in the interior of $\angle\text{AOD}.$
Answer
True.
Point $C$ lies in the interior of angle $AOD.$
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Question 211 Mark
Measure of the following angles with the help of a protractor and write the measure in degrees:
Answer
Place the protractor in such a way that its centre is exactly at the vertex $O$ of the given angle $AOB$ and the base line lies along the arm $OA$. Read off the mark through which the arm $OB$ passes, starting from $0^\circ $ on the side $A.$

We find that $\angle\text{AOB}=45^\circ.$
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Question 221 Mark
Classify the angles whose magnitudes are given below:
$(38.3)^\circ $
Answer
Acute angle.
This is because its measure is more than $0^\circ $ but less than $90^\circ $
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Question 231 Mark
State the type of the following angles:
Answer
$\angle\text{POQ}$ is a reflex angle since its measure is more than $180^\circ $ but less than $360^\circ .$
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Question 251 Mark
Classify the angles whose magnitudes are given below:
$0^\circ $
Answer
Zero angle.
This is because its measure is zero.
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Question 261 Mark
Classify the angles whose magnitudes are given below: $360^\circ $
Answer
Complete angle. This is because its measure is $360^\circ $
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Question 281 Mark
Name the vertex and the arms of $\angle\text{ABC},$ given in the figure below.
Answer
In the given angle $ABC,$ the vertex is $B$ and arms are $\vec{\text{AB}}\text{ and }\vec{\text{BC}}.$
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Question 291 Mark
Classify the angles whose magnitudes are given below: $15^\circ $
Answer
Acute angle. This is because its measure is more than $0^\circ $ but less than $90^\circ $
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Question 301 Mark
Classify the angles whose magnitudes are given below: $30^\circ $
Answer
Acute angle. This is because its measure is less than $90^\circ $ but more than $0^\circ $
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Question 321 Mark
How many angles are formed in the figures given below? Name them.
Answer
In the given figure, four angles are formed.
$\angle\text{ABC},\angle\text{BCD},\angle\text{CDA and }\angle\text{BAD}$
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Question 331 Mark
How many degrees are there in the angle between the hour hand and the minute hand of a clock, when it is: $6$ o'clock?
Answer
$180^\circ .$
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Question 341 Mark
Classify the angles whose magnitudes are given below: $(90.5)^\circ $
Answer
Obtuse angle. This is because its measure is more than $90^\circ $ but less than $180^\circ $
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Question 361 Mark
See the adjacent figure and state the following statement are true and false.

Point $C$ lies on $\angle\text{AOB}.$
Answer
False.
Point $C$ lies in the interior of angle $AOB.$
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Question 381 Mark
Classify the angles whose magnitudes are given below: $181^\circ $
Answer
Reflex angle. This is because its measure is more than $180^\circ $ but less than $360^\circ $.
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Question 391 Mark
Classify the angles whose magnitudes are given below: $90^\circ $
Answer
Right angle. This is because its measure is $90^\circ $
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Question 401 Mark
How many degrees are there in the angle between the hour hand and the minute hand of a clock, when it is: $12$ o'clock?
Answer
$0^\circ .$
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Question 411 Mark
Measure of the following angles with the help of a protractor and write the measure in degrees:
Answer
The given angle is $\angle\text{GHI}.$ Place the protractor in such a way that its centre is exactly on the vertex $H$ of the given angle and the base line lies along the arm $HI$. Read off the mark through which the arm $HG$ passes, starting from $0^\circ $ on the side of $I$.

We find that $\angle\text{GHI}= 70^\circ.$
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Question 421 Mark
State the type of the following angles:
Answer
$\angle\text{COD}$ is a right angle since its measure is $90^\circ .$
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