Tag: mathematics and statistics

Questions Related to mathematics and statistics

Mark the correct alternative of the following.
An angle of measure $360^o$ is called?

mathematics and statistics angle and its measurement directed angles

  1. A zero angle

  2. A straight angle

  3. A reflex angle

  4. A complete angle

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Correct Option: D
Explanation:

An angle of measure $360^o$ is called a complete angle. [ Using definition of complete angle]

 Angles of a triangle are in the ratio $3 : 4 : 5$. The smallest angle is $45^o$.

mathematics and statistics angle and its measurement directed angles

  1. True

  2. False

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Correct Option: A
Explanation:

Angles of the triangle are in the ratio $3 : 4: 5$
Let the angles be $3x, 4x$ and $5x$
Sum of the angles of the triangle $= 180$
Thus, $3x + 4x + 5x = 180$
$12x = 180$
$x = 15$
Thus, the angles are $45^{o}, 60^{o}$ and $75^{o}$.

Mark the correct alternative of the following.
In a $\Delta ABC$, if $\angle A-\angle B=33^o$ and $\angle B-\angle C=18^o$, then $\angle B=?$

mathematics and statistics angle and its measurement directed angles

  1. $35^o$

  2. $45^o$

  3. $56^o$

  4. $55^o$

Show answer
Correct Option: D
Explanation:

Given,

$\angle A-\angle B=33^o$.....(1) and $\angle B-\angle C=18^o$.....(2).
Now subtracting  (2) from (1) we get,
$\angle A-2\angle B+\angle C=15^o$.....(3).
We've, $\angle A+\angle B+\angle C=180^o$....(4).
Now subtracting (4) from (3) we get,
$3\angle B=180^o-15^o$
or, $3\angle B=165^o$
or, $\angle B=55^o$.

The two rays of an angle are called 

mathematics and statistics angle and its measurement directed angles

  1. lines of the angle

  2. two sides of the angle

  3. two parts of the angle

  4. none

Show answer
Correct Option: B
Explanation:

The two rays of an angle $=$ 2 sides of the angle 

The maximum number of letters that can be used to represent an angle are

mathematics and statistics angle and its measurement directed angles

  1. $5$

  2. $2$

  3. $3$

  4. $1$

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Correct Option: C
Explanation:

The maximum number of letters that can be used to represent an angle are $3$

The two rays of an angle are called

mathematics and statistics angle and its measurement directed angles

  1. lines of the angle

  2. two sides of the angle

  3. two parts of the angle

  4. none of these

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Correct Option: B
Explanation:

The two rays of an angle are called two sides of the angle

Which of the following statements is correct?

mathematics and statistics angle and its measurement directed angles

  1. A triangle has two right angles.

  2. All the angles of a triangle are more than 60$^o$

  3. An exterior angle of a triangle is always greater than the opposite interior angles.

  4. All the angles of a triangle are less than 60$^o$

Show answer
Correct Option: C
Explanation:

We know, The interior angles of a triangle always add up to 180.
So,  statement A, B and C is not correct.
(C) An exterior angle of a triangle is always greater than the opposite interior angles.
 is correct
Answer (C) An exterior angle of a triangle is always greater than the opposite interior angles.

If a bicycle wheel has 48 spokes the angle between the adjacent pair spokes is :

mathematics and statistics angle and its measurement directed angles

  1. $\left ( 6\frac{1}{2} \right )^0$

  2. $\left ( 7\frac{1}{2} \right )^0$

  3. $\left ( 7\frac{1}{3} \right )^0$

  4. $\left ( 6\frac{2}{3} \right )^0$

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Correct Option: B
Explanation:

required angle = $\frac{360}{48}$
$\frac{30}{4}$ = $\frac{15}{2}$= $\left ( 7\frac{1}{2} \right )^0$

The number of triangles with any three of the length 1, 4, 6 and 8 cm, as sides is

mathematics and statistics angle and its measurement directed angles

  1. 4

  2. 2

  3. 1

  4. 0

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Correct Option: C
Explanation:

Since in a triangle sum of any two sides is greater than or equal to third one.
If we take length 1,4 and 6 cm, then $4+1=5$cm is not greater than or equal 6.
If we take length 1,4 and 8 cm, then $4+1=5$cm is not greater than or equal 8.
If we take length 1,6 and 8 cm, then $6+1=7$cm is not greater than or equal 8.
But if  we take length 4,6 and 8 cm, then above property hold.
Therefore, only one triangle possible.
Option C is correct.

The measure of an angle which is five times its supplement is

mathematics and statistics angle and its measurement directed angles

  1. $36^0$

  2. $30^0$

  3. $150^0$

  4. $180^0$

Show answer
Correct Option: B
Explanation:

Let, required angle is =x

Supplementary angle of x is =${{180}^{0}}-x$

Now, according to question,

$ 5\times x={{180}^{0}}-x $

$ 6x={{180}^{0}} $

$ x={{30}^{0}} $


Hence, this is the answer.