Tag: angle and its measurement

Quizzes (5) Questions (46)

Questions Related to angle and its measurement

Multiple choice mathematics and statistics angle and its measurement directed angles

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

  1. $3x+y =16$
  2. $x - 3y =12$
  3. $x+ 3y =16$
  4. $3x - y =12$
Reveal answer Fill a bubble to check yourself
C Correct answer
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,
$\Rightarrow$  $y-4=\dfrac{-1}{3}(x-4)$

$\Rightarrow$  $3y-12=-x+4$

$\Rightarrow$  $x+3y=16$

Multiple choice mathematics and statistics angle and its measurement directed angles

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

  1. A zero angle

  2. A straight angle

  3. A reflex angle

  4. A complete angle
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

Multiple choice mathematics and statistics angle and its measurement directed angles

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $75^{o}$.