Rs Aggarwal 2020 2021 Solutions for Class 8 Maths Chapter 14 Polygons are provided here with simple step-by-step explanations. These solutions for Polygons are extremely popular among Class 8 students for Maths Polygons Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2020 2021 Book of Class 8 Maths Chapter 14 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2020 2021 Solutions. All Rs Aggarwal 2020 2021 Solutions for class Class 8 Maths are prepared by experts and are 100% accurate.

#### Page No 182:

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:

#### Page No 182:

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°.

#### Page No 182:

For a regular polygon with n sides:

(i) For a polygon with 10 sides:

(ii) For a polygon with 15 sides:

#### Page No 182:

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°.

#### Page No 182:

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:

#### Page No 182:

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:

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

#### Page No 182:

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

(i)

(ii)

(iii)

(iv)

#### Page No 182:

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

∴ x = 105

#### Page No 182:

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

∴ x = 108

#### Page No 182:

(a) 5

For a pentagon:
$n=5$

#### Page No 182:

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

#### Page No 182:

(d) 20

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

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

#### Page No 182:

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

(c) 9

#### Page No 183:

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

(b) 9

#### Page No 183:

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

(a) 8

#### Page No 183:

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

#### Page No 183:

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

#### Page No 183:

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

(a) 135°

#### Page No 183:

(d) 10

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