Tag: measurement of an angle

Questions Related to measurement of an 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. $59^o$

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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

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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

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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.

Two triangles are similar, if their corresponding angles are ________.

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

  1. Proportional

  2. Equal

  3. A & B

  4. None of the above

Show answer
Correct Option: B
Explanation:

Two triangles are similar, if their corresponding angles are equal.

(Two triangles are similar, if their corresponding angles are equal and corresponding sides are proportional.)