Tag: directed angles

Quizzes (0) Questions (45)

Questions Related to directed angles

Multiple choice mathematics and statistics angle and its measurement directed angles

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 $\angle B=?$

  1. $35^o$
  2. $45^o$
  3. $56^o$
  4. $55^o$
Reveal answer Fill a bubble to check yourself
D Correct answer
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, $\angle B=55^o$.

Multiple choice mathematics and statistics angle and its measurement directed angles

Which of the following statements is correct?

  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$^o$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

Multiple choice mathematics and statistics angle and its measurement directed angles

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

  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. $\left ( 6\frac{2}{3} \right )^0$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

Multiple choice mathematics and statistics angle and its measurement directed angles

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

  1. 4

  2. 2

  3. 1

  4. 0
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

Multiple choice mathematics and statistics angle and its measurement directed angles

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

  1. $36^0$
  2. $30^0$
  3. $150^0$
  4. $180^0$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

Multiple choice mathematics and statistics angle and its measurement directed angles

In $\displaystyle \angle ROP,$ the vertex is at:

  1. $R$
  2. $P$
  3. $O$

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Here, the angle is written as $\angle{ROP}$ and the angle is made by the intersection of two lines. 

So, here $RO$ and $OP$ are two lines which makes the angle at point $O$.
Hence, the vertex is at $O$.