Tag: angle and its measurement

Questions Related to angle and its measurement

If $P,Q,R$ and $S$ are $(1,2,5),(-2,1,3),(4,4,2)$ and $(2,1,-4)$, then projection of $PQ$ on $RS$ be

mathematics and statistics angle and its measurement directed angles

  1. $2$

  2. $3$

  3. $4$

  4. $5$

Show answer
Correct Option: C

The number of right angles $ABC$ that can be formed is 

mathematics and statistics angle and its measurement directed angles

  1. $0$

  2. $1$

  3. $2$

  4. $4$

Show answer
Correct Option: B
Explanation:

$1$


as sum of angles in a triangle should be $180$

only one angle can be a right angle.

A triangle has ____ exterior angles.

mathematics and statistics angle and its measurement directed angles

  1. two

  2. three

  3. four

  4. six

Show answer
Correct Option: D
Explanation:

A triangle has 3 sides, 3 vertices, at these each vertices, we get 2 exterior angles,


therefore, $3 \times 2 = 6$ exterior angles.

The measure of co-terminal angle differ by an integral multiple of_________

mathematics and statistics angle and its measurement directed angles

  1. $90^{o}$

  2. $180^{o}$

  3. $360^{o}$

  4. $270^{o}$

Show answer
Correct Option: A

The ratio between the complementary and the supplementary angles of an angle is $1:7$. What is the measure of that angle?

mathematics and statistics angle and its measurement directed angles

  1. $15^o$

  2. $75^o$

  3. $60^o$

  4. $65^o$

Show answer
Correct Option: A

The equation to the perpendicular bisector of the line segment joining (5,7) (3,1) is 

mathematics and statistics angle and its measurement directed angles

  1. $3x+y =16$

  2. $x - 3y =12$

  3. $x+ 3y =16$

  4. $3x - y =12$

Show answer
Correct Option: C
Explanation:

Here, $A=(5,7)$ and $B=(3,1)$


Here, $x _1=5,y _1=7,x _2=3$ and $y _2=1$


$\Rightarrow$  Mid-point of $A$ and $B=$ $\left(\dfrac{x _1+x _2}{2},\dfrac{y _1+y _2}{2}\right)$

                                            $=\left(\dfrac{5+3}{2},\dfrac{7+1}{2}\right)$

                                            $=\left(4,4\right)$

$\Rightarrow$  Slope of $AB\,(m)=\dfrac{1-7}{3-5}=\dfrac{-6}{-2}=3$

$\Rightarrow$  Slope of the perpendicular $(m _1)$ $=\dfrac{-1}{m}=\dfrac{-1}{3}$

The perpendicular passes through $(4,4)$.

The equation is,
$\Rightarrow$  $y-4=\dfrac{-1}{3}(x-4)$

$\Rightarrow$  $3y-12=-x+4$

$\Rightarrow$  $x+3y=16$

Mark the correct alternative of the following.
An angle of measure $0^o$ is called?

mathematics and statistics angle and its measurement directed angles

  1. A complete angle

  2. A right angle

  3. A straight angle

  4. None of these

Show answer
Correct Option: D
Explanation:

An angle of measure $0^o$ is called a zero degree angle.

Mark the correct alternative of the following.
An angle of measure $90^o$ is called?

mathematics and statistics angle and its measurement directed angles

  1. A complete angle

  2. A right angle

  3. A straight angle

  4. A reflex angle

Show answer
Correct Option: B
Explanation:

An angle of measure $90^o$ is called a right angle.

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

Show answer
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

Show answer
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 $75^{o}$.