Tag: polygons

Questions Related to polygons

Find the measure of exterior angle of a regular polygon of 9 sides

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

  1. $40^o$

  2. $60^o$

  3. $50^o$

  4. $30^o$

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Correct Option: A
Explanation:

Each exterior angle of a regular polygon of 9 sides
$=\dfrac {360^o}{n}$, where $n=9=\left (\dfrac {360^o}{9}\right )^o=40^o$

If the sum of all interior angles of a convex polygon is 1440, then the number of sides of the polygon is

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

  1. 8

  2. 10

  3. 11

  4. 12

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Correct Option: B
Explanation:

If n is the number of sides of the polygon, then $(2n -4)\times 90^o = 1440$
or 2n = 20          or          n = 10

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

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

  1. $\displaystyle 4040^{\circ}$

  2. $\displaystyle 5040^{\circ}$

  3. $\displaystyle 6040^{\circ}$

  4. $\displaystyle 7040^{\circ}$

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Correct Option: B
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=$180(n-2)=180(30-2)=5040^{0}$

The measure of the external angle of a regular hexagon is 

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

  1. ${\pi/3}$

  2. ${\pi/4}$,

  3. ${\pi/6}$

  4. None

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Correct Option: A
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 $=60^o\times \dfrac{\pi}{180^o}=\dfrac{\pi}{3}$ 

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

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

  1. not possible

  2. possible

  3. cannot be determined

  4. none of the above

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Correct Option: A
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.

The measure of the external angle of a regular octagon is 

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

  1. ${\pi/4}$

  2. ${\pi/6}$

  3. ${\pi/8}$

  4. ${\pi/12}$

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Correct Option: A
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 $\dfrac{\pi}{4}$

Each exterior angle of a regular hexagon is of

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

  1. $120^\circ$

  2. $80^\circ$

  3. $100^\circ$

  4. $60^\circ$

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Correct Option: D

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

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

  1. $10$

  2. $8$

  3. $9$

  4. $13$

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Correct Option: B
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
$\Rightarrow \dfrac{360}{n}=\dfrac{1}{3} \left (180-\dfrac{360}{n}\right)$
$\Rightarrow n=8$

The number of sides of a regular polygon whose each exterior angle has a measure of $45^o$ is __________.

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

  1. $4$

  2. $6$

  3. $8$

  4. $10$

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Correct Option: C
Explanation:

The exterior angle of a regular polygon is $\dfrac{360}{n}$.

Given, $45^\circ$
$\Rightarrow \dfrac{360}{n}=45$

$\Rightarrow n=8$

The measure of each exterior angle of an n-sided regular polygon is $(\dfrac{180^0}{n})$.

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

  1. True

  2. False

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Correct Option: A