Tag: construction of angles

Questions Related to construction of angles

At what time is the angle between the hands of a clock equal to $30^{o}$ ?

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $1:00$

  2. $11:00$

  3. $2:00$

  4. $12:00$

Show answer
Correct Option: A,B
Explanation:

A clock is a circle made of $360^\circ$, and that each hour represents an angle and the separation between them is $\dfrac{360^\circ}{12}=30^\circ$


Hence, 
At $1:00$ the angle between the hands is $30^\circ$, minute hand pointing at 12 and hour hand at 1.

Similarly
At $11:00$ the angle between the hands is $30^\circ$

At $2:00$ the angle between the hands is $60^\circ$

At $12:00$ the angle between the hands is $0^\circ$

How many times between $6:00$ am and $6:00$ pm, do the hands of a clock make a straight line 

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $9$

  2. $10$

  3. $11$

  4. $12$

Show answer
Correct Option: C
Explanation:
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours.

 (Because between 5 and 7 they point in opposite directions at 6 o'clock only).

So between $6:00$ am to $6:00$ pm ($12$ hours), $11$ times hands of a clock make a straight line.

How many times in a day, do the hands of a clock make a right angle ?

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $21$

  2. $22$

  3. $42$

  4. $44$

Show answer
Correct Option: D
Explanation:

There will be $2$ times per hour when the angle between minute and hour hand is $90^\circ$

Total of $22$ times in $12$ hours.
$\therefore$ In $24$ hours, $22\times 2=44$ times the angle between minute and hour hand is $90^\circ$.

At 2:15 o'clock, the hour and minute hands of a clock form an angle of:

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $30^{\circ}$

  2. $5^{\circ}$

  3. $22\dfrac{1}{2}{\circ}$

  4. $7\dfrac{1}{2}{\circ}$

Show answer
Correct Option: C
Explanation:
   $\underset { \downarrow  }{ \underline { 2 }  } <2:15<\underset { \downarrow  }{ 3 } $' $O$ clock
$\left( { 60 }^{ 0 } \right) $             $\left( { 90 }^{ 0 } \right) $
when minute hand rotates $15$ min hour hand rotate $\dfrac { 15 }{ 60 } \times { 30 }^{ 0 }={ 7.5 }^{ 0 }$
So, angle at $2:15$ is $=\left( { 90 }^{ 0 }-\left( { 60 }^{ 0 }+{ 7.5 }^{ 0 } \right)  \right) ={ 22.5 }^{ 0 }$

Say True or False.
The measure of an obtuse angle $< 90^o$.

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

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

False
The measure of an obtuse angle is greater than $90^o$ but less than $180^o$.

An angle whose measure is the sum of the measures of two right angles is _______.

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

  1. Acute

  2. Obtuse

  3. Right

  4. Straight

Show answer
Correct Option: D
Explanation:

Measure of a right angle is $90^ \circ$

Measure of a straight angle is $180^ \circ$
Sum of the measure of two right angles is $(90+90)^ \circ=180^ \circ$
Thus an angle whose measure is the sum of two right angles is $Straight$

An angle whose measure is greater than that of a right angle is ______.

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

  1. Acute

  2. Obtuse

  3. Right

  4. Straight

Show answer
Correct Option: B
Explanation:

$Obtuse \ angle$ has measure more than that of $right \ angle \ but \ less \ than \ 180\ degree$

Hence correct answer is $B) \ Obtuse$

An angle whose measure is less than that of a right angle is ______.

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

  1. Acute

  2. Obtuse

  3. Right

  4. Straight

Show answer
Correct Option: A
Explanation:

$Acute \ angle$ has measure less than $right \ angle$

Hence correct answer is $A) \ Acute$

$\displaystyle 89^{\circ}$ is an example of :

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

  1. obtuse

  2. acute

  3. right

  4. None of the above

Show answer
Correct Option: B
Explanation:

Angles between $ {0}^{o} $ and $ {90}^{o} $ are acute angles. Hence, $ {89}^{o} $ is an acute angle.

Based on the angle measures given, which triangle is not acute?

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

  1. $35^\circ,\, 69^\circ,\, 76^\circ$

  2. $60^\circ,\, 60^\circ,\, 60^\circ$

  3. $88^\circ,\, 46^\circ,\, 46^\circ$

  4. $90^\circ,\, 45^\circ,\, 45^\circ$

Show answer
Correct Option: D
Explanation:

For acute angles triangle all the three angles must be less than ${ 90 }^{ \circ  }$.

In option $D$ one of the angle is ${ 90 }^{ \circ  }$ , so it is not acute angles triangle.