Tag: types of angle

Questions Related to types of angle

The difference between two angles is $19$$\displaystyle ^{o}$ and their sum is $\displaystyle \frac{890}{9}^o$. Find the greater angle.

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

  1. $63^o$

  2. $35^o$

  3. $27^o$

  4. $59^o$

Show answer
Correct Option: D
Explanation:
Let the two angles be $a$ and $b$

Then, 
$a  - b = 19$

and, $a + b = \dfrac{890}{9}$

Adding the two equations,

$2a = \dfrac{890 + 19\times 9}{9}$

$2a = \dfrac{1061}{9}$

Thus, $a = \dfrac{1061}{18}$

$a \approx 59^{\circ}$

If two angles of a triangle are acute angles, the third angle:

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

  1. is less than the sum of the two angles

  2. is an acute angle

  3. is the largest angle of the triangle

  4. may be an obtuse angle

Show answer
Correct Option: D
Explanation:
For a triangle $ABC$, sum of angles is $180^0$
Two angles are given as acute, $\angle A, \angle B < 90^0$
$\angle A = 90^0 - x$
$\angle B = 90^0 - y$
where, $x,y < 90^0$
$\therefore \angle A + \angle B+ \angle C = 180^0$
$\Rightarrow \angle C = x+y $
$x+y$ can be $>90^0$ or $<90^0$
So, it may be obtuse or acute.
Hence, option D.

An angle which measures $\displaystyle 0^{o}$ is called:

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

  1. obtuse angle

  2. straight angle

  3. zero angle

  4. right angle

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Correct Option: C
Explanation:

An angle which measure $0^0$ is called zero angle.

An angle which measure more than $0^o$ and less than $90^o$ is an acute angle.
An angle which measures $90^o$ is called a right angle.
An angle which measure more than $90^o$ and less than $180^o$ is an obtuse angle.

Hence, the answer is zero angle.

Find the supplement  of the following angle.
$40^{\circ}$

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

  1. $140$

  2. $40$

  3. $10$

  4. None of these

Show answer
Correct Option: A
Explanation:

We know that the supplement angle

$=180^0-\theta$

So,
The supplement angle of $40^0$ will be
$=180^0-40^0=140^0$ 

Hence, this is the answer.

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

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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.