Tag: sum of exterior angles of polygons

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Multiple choice maths polygons exterior angles of polygon sum of exterior angles of polygons exterior angles of a polygon

An exterior angle of regular polygon is $\displaystyle 12^{\circ}$ the sum of all the interior angles is

  1. $\displaystyle 4040^{\circ}$
  2. $\displaystyle 5040^{\circ}$
  3. $\displaystyle 6040^{\circ}$
  4. $\displaystyle 7040^{\circ}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given the exterior angle of regular polygon is 12

We know each  exterior angle of regular polygon=$\dfrac{360}{n}$ where n is the sides of polygon
$\dfrac{360}{n}=12\Rightarrow n=30$
we know that interior angle of  regular polygon=$180(n-2)=180(30-2)=5040^{0}$

Multiple choice maths polygons exterior angles of polygon sum of exterior angles of polygons exterior angles of a polygon

The measure of the external angle of a regular hexagon is 

  1. ${\pi/3}$
  2. ${\pi/4}$,
  3. ${\pi/6}$

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$ Sum of exterior angles of a regular hexagon $=360^o$

$\Rightarrow$  Number of sides of regular hexagon $=6$
$\Rightarrow$  The measure of the external angle of a regular hexagon $=\dfrac{360^o}{6}=60^o$
In radian $=60^o\times \dfrac{\pi}{180^o}=\dfrac{\pi}{3}$ 

Multiple choice maths polygons exterior angles of polygon sum of exterior angles of polygons exterior angles of a polygon

Is it possible to have a regular polygon with measure of each exterior angle as $22^o$?

  1. not possible

  2. possible

  3. cannot be determined

  4. none of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Since the number of sides of a regular polygon
$=\dfrac {360}{\text {Exterior angle}}$
$\therefore$ The number of sides of a regular polygon
$=\dfrac {360}{22}[\because$ Exterior angle $=22^o$, given]
$=\dfrac {180}{11}$
Which is not a whole number.
$\therefore$ A regular polygon with measure of each exterior angle as $22^o$ is not possible.

Multiple choice maths polygons exterior angles of polygon sum of exterior angles of polygons exterior angles of a polygon

The measure of the external angle of a regular octagon is 

  1. ${\pi/4}$
  2. ${\pi/6}$
  3. ${\pi/8}$
  4. ${\pi/12}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  The sum of the exterior angles of regular octagon is $360^o$.

$\Rightarrow$ Number of sides of octagon $=8$
$\Rightarrow$  The measure of the external angles $=\dfrac{360^o}{8}=45^o$
In radian $=45^o\times \dfrac{\pi}{180^o}=\dfrac{\pi}{4}$
$\therefore$  The measure of the external angle of a regular octagon is $\dfrac{\pi}{4}$

Multiple choice maths polygons exterior angles of polygon sum of exterior angles of polygons exterior angles of a polygon

The exterior angle of a regular polygon is one-third of its interior angle. How many sides does the polygon has?

  1. $10$
  2. $8$
  3. $9$
  4. $13$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let no of sides of the polygon is $n$ 

Exterior angle will be $\dfrac{360}{n}$
Interior angle will be $\left ( 180-\dfrac{360}{n}\right)$
Exterior angle is $\dfrac{1}{3}$ of the interior angle
$\Rightarrow \dfrac{360}{n}=\dfrac{1}{3} \left (180-\dfrac{360}{n}\right)$
$\Rightarrow n=8$