Rs Aggarwal 2017 Solutions for Class 8 Math Chapter 14 Polygons are provided here with simple step-by-step explanations. These solutions for Polygons are extremely popular among Class 8 students for Math Polygons Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2017 Book of Class 8 Math Chapter 14 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2017 Solutions. All Rs Aggarwal 2017 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

#### Question 1:

Find the measure of each exterior angle of a regular
(i) pentagon
(ii) hexagon
(iii) heptagon
(iv) decagon
(v) polygon of 15 sides.

Exterior angle of an n-sided polygon = ${\left(\frac{360}{n}\right)}^{o}$
(i) For a pentagon:

(ii) For a hexagon:

(iii) For a heptagon:

(iv) For a decagon:

(v) For a polygon of 15 sides:

#### Question 2:

Is it possible to have a regular polygon each of whose exterior angles is 50°?

Each exterior angle of an n-sided polygon = ${\left(\frac{360}{n}\right)}^{o}$
If the exterior angle is 50°, then:

Since n is not an integer, we cannot have a polygon with each exterior angle equal to 50°.

#### Question 3:

Find the measure of each interior angle of a regular polygon having
(i) 10 sides
(ii) 15 sides.

For a regular polygon with n sides:

(i) For a polygon with 10 sides:

(ii) For a polygon with 15 sides:

#### Question 4:

Is it possible to have a regular polygon each of whose interior angles is 100°?

Each interior angle of a regular polygon having n sides =

If each interior angle of the polygon is 100°, then:

Since n is not an integer, it is not possible to have a regular polygon with each interior angle equal to 100°.

#### Question 5:

What is the sum of all interior angles of a regular
(i) pentagon
(ii) hexagon
(iii) nonagon
(iv) polygon of 12 sides?

Sum of the interior angles of an n-sided polygon = $\left(n-2\right)×180°$

(i) For a pentagon:

(ii) For a hexagon:

(iii) For a nonagon:

(iv) For a polygon of 12 sides:

#### Question 6:

What is the number of diagonals in a
(i) heptagon
(ii) octagon
(iii) polygon of 12 sides?

Number of diagonal in an n-sided polygon = $\frac{n\left(n-3\right)}{2}$
(i) For a heptagon:

$n=7⇒\frac{n\left(n-3\right)}{2}=\frac{7\left(7-3\right)}{2}=\frac{28}{2}=14$

(ii) For an octagon:

$n=8⇒\frac{n\left(n-3\right)}{2}=\frac{8\left(8-3\right)}{2}=\frac{40}{2}=20$

(iii) For a 12-sided polygon:

$n=12⇒\frac{n\left(n-3\right)}{2}=\frac{12\left(12-3\right)}{2}=\frac{108}{2}=54$

#### Question 7:

Find the number of sides of a regular polygon whose each exterior angle measures:
(i) 40°
(ii) 36°
(iii) 72°
(iv) 30°

Sum of all the exterior angles of a regular polygon is ${360}^{o}$​.

(i)

(ii)

(iii)

(iv)

#### Question 8:

In the given figure, find the angle measure x. Sum of all the interior angles of an n-sided polygon = $\left(n-2\right)×180°$

∴ x = 105

#### Question 9:

Find the angle measure x in the given figure. For a regular n-sided polygon:
Each interior angle = $180-\left(\frac{360}{n}\right)$
In the given figure:

∴ x = 108

#### Question 1:

How many diagonals are there in a pentagon?
(a) 5
(b) 7
(c) 6
(d) 10

(a) 5

For a pentagon:
$n=5$

#### Question 2:

How many diagonals are there in a hexagon?
(a) 6
(b) 8
(c) 9
(d) 10

(c) 9
Number of diagonals in an n-sided polygon = $\frac{n\left(n-3\right)}{2}$
For a hexagon:

#### Question 3:

How many diagonals are there in an octagon?
(a) 8
(b) 16
(c) 18
(d) 20

(d) 20

​For a regular n-sided polygon:
Number of diagonals =: $\frac{n\left(n-3\right)}{2}$
For an octagon:

$n=8\phantom{\rule{0ex}{0ex}}\frac{8\left(8-3\right)}{2}=\frac{40}{2}=20$

#### Question 4:

How many diagonals are there in a polygon having 12 sides?
(a) 12
(b) 24
(c) 36
(d) 54

(d) 54
For an n-sided polygon:
Number of diagonals = $\frac{n\left(n-3\right)}{2}$

#### Question 5:

A polygon has 27 diagonals. How many sides does it have?
(a) 7
(b) 8
(c) 9
(d) 12

(c) 9

#### Question 6:

The angles of a pentagon are x°, (x + 20)°, (x + 40)°, (x + 60)° and (x + 80)°. The smallest angle of the pentagon is
(a) 75°
(b) 68°
(c) 78°
(d) 85°

(b) 68°
​Sum of all the interior angles of a polygon with n sides = $\left(n-2\right)×180°$

#### Question 7:

The measure of each exterior angle of a regular polygon is 40°. How many sides does it have?
(a) 8
(b) 9
(c) 6
(d) 10

(b) 9

#### Question 8:

Each interior angle of a polygon is 108°. How many sides does it have?
(a) 8
(b) 6
(c) 5
(d) 7

(c) 5
​Each interior angle for a regular n-sided polygon = $180-\left(\frac{360}{n}\right)$

#### Question 9:

Each interior angle of a polygon is 135°. How many sides does it have?
(a) 8
(b) 7
(c) 6
(d) 10

(a) 8

#### Question 10:

In a regular polygon, each interior angle is thrice the exterior angle. The number os sides of the polygon is
(a) 6
(b) 8
(c) 10
(d) 12

(b) 8
For a regular polygon with n sides:
Each exterior angle = $\frac{360}{n}$
Each interior angle = $180-\frac{360}{n}$

#### Question 11:

Each interior angle of a regular decagon is
(a) 60°
(b) 120°
(c) 144°
(d) 180°

(c) 144°
Each interior angle of a regular decagon = $180-\frac{360}{10}=180-36={144}^{o}$

#### Question 12:

The sum of all interior angles of a hexagon is
(a) 6 right ∠s
(b) 8 right ∠s
(c) 9 right ∠s
(d) 12 right ∠s

(b)
Sum of all the interior angles of a hexagon is $\left(2n-4\right)$ right angles.
For a hexagon:

#### Question 13:

The sum of all interior angles of a regular polygon is 1080°. What is the measure of each of its interior angles?
(a) 135°
(b) 120°
(c) 156°
(d) 144°

(a) 135°