Mathematics

Polygons and Angles

100 Questions

Polygons and angles focus on calculating interior and exterior angle sums. Questions also cover properties of regular shapes like hexagons and nonagons. This geometry topic is essential for quantitative aptitude sections in major competitive exams.

Interior angle sumsExterior angle sumsRegular polygonsPolygon propertiesTriangle formation

Polygons and Angles Questions

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

State true or false.
Is it possible to have a regular polygon whose each exterior angle is $32^{\circ}$

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given, a regular polygon whose each exterior angle is $32^o $
Each exterior angle of a regular polygon = $ \dfrac {360^o}{n} $, where n = number of side
Now,
$ \dfrac {360^o}{n} = 32^o $
$=> n = \dfrac{45}{4} $
Since, n should be an integer, so it is not possible a regular polygon whose each exterior angle is $32^o $

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

State true or false: 
Is it possible to have a regular polygon whose each exterior angle is $80^o$
80∘

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the number of sides of the polygon is n. (which must be an integer)
If each exterior angle is $ 80^o $, then sum of all exterior angle is $ n \times 80^o $.
And Sum of all exterior angles = $ 180^o $
$=>  n \times 80^o = 180^o $
$=> n = 1.25 $
So, it is not possible to have a regular polygon whose each exterior angle is $ 80^o $

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

State true or false.
Is it possible to have a regular polygon whose each exterior angle is $20^{\circ}$

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given, a regular polygon whose each exterior angle is $20^o $
Each exterior angle of a regular polygon = $ \dfrac {360^o}{n} $, where n = number of side
Now,
$ \dfrac {360^o}{n} = 20^o $
$=> n = 18 $
Since, n should be an integer, so their exist a regular polygon whose each exterior angle is $20^o $

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