myhelper: RS Aggarwal solution class 8 chapter 14 Polygons Exercise 14B

Exercise 14B

Q1 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 1:

Tick (✓) the correct answer:
How many diagonals are there in a pentagon?
(a) 5
(b) 7
(c) 6
(d) 10

Answer 1:

(a) 5

For a pentagon:
$n = 5$

$Number of diagonals = \frac{n (n - 3)}{2} = \frac{5 (5 - 3)}{2} = 5$

Q2 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 2:

Tick (✓) the correct answer:
How many diagonals are there in a hexagon?
(a) 6
(b) 8
(c) 9
(d) 10

Answer 2:

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

$n = 6 ∴ \frac{n (n - 3)}{2} = \frac{6 (6 - 3)}{2} = \frac{18}{2} = 9$

Q3 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 3:

Tick (✓) the correct answer:
How many diagonals are there in an octagon?
(a) 8
(b) 16
(c) 18
(d) 20

Answer 3:

(d) 20

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

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

Q4 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 4:

Tick (✓) the correct answer:
How many diagonals are there in a polygon having 12 sides?
(a) 12
(b) 24
(c) 36
(d) 54

Answer 4:

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

$∴ n = 12 \Rightarrow \frac{12 (12 - 3)}{2} = 54$

Q5 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 5:

Tick (✓) the correct answer:
A polygon has 27 diagonals. How many sides does it have?
(a) 7
(b) 8
(c) 9
(d) 12

Answer 5:

(c) 9

$\frac{n (n - 3)}{2} = 27 \Rightarrow n (n - 3) = 54 \Rightarrow n^{2} - 3 n - 54 = 0 \Rightarrow n^{2} - 9 n + 6 n - 54 = 0 \Rightarrow n (n - 9) + 6 (n - 9) = 0 \Rightarrow n = - 6 o r n = 9 Number of sides cannot be negative . ∴ n = 9$

Page-183

Q6 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

OPEN IN YOUTUBE

Question 6:

Tick (✓) the correct answer:
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°

Answer 6:

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

$∴ (5 - 2) \times 180 °= x + x + 20 + x + 40 + x + 60 + x + 80 \Rightarrow 540 = 5 x + 200 \Rightarrow 5 x = 340 \Rightarrow x = 68$ °

Q7 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

OPEN IN YOUTUBE

Question 7:

Tick (✓) the correct answer:
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

Answer 7:

(b) 9
$Each exterior angle of a regular n - sided polygon = \frac{360}{n} = 40 \Rightarrow n = \frac{360}{40} = 9$

Q8 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

OPEN IN YOUTUBE

Question 8:

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

Answer 8:

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

$180 - (\frac{360}{n}) = 108 \Rightarrow (\frac{360}{n}) = 72 \Rightarrow n = \frac{360}{72} = 5$

Q9 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

OPEN IN YOUTUBE

Question 9:

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

Answer 9:

(a) 8
$Each interior angle of a regular polygon with n sides = 180 - (\frac{360}{n}) \Rightarrow 180 - (\frac{360}{n}) = 135 \Rightarrow \frac{360}{n} = 45 \Rightarrow n = 8$

Q10 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

OPEN IN YOUTUBE

Question 10:

Tick (✓) the correct answer:
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

Answer 10:

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

$∴ 180 - \frac{360}{n} = 3 (\frac{360}{n}) \Rightarrow 180 = 4 (\frac{360}{n}) \Rightarrow n = \frac{4 \times 360}{180} = 8$

Q11 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

OPEN IN YOUTUBE

Question 11:

Tick (✓) the correct answer:
Each interior angle of a regular decagon is
(a) 60°
(b) 120°
(c) 144°
(d) 180°

Answer 11:

Q12 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

OPEN IN YOUTUBE

Question 12:

Tick (✓) the correct answer:
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

Answer 12:

(b) $8 r i g h t ∠ s$
Sum of all the interior angles of a hexagon is $(2 n - 4)$ right angles.
For a hexagon:
$n = 6 \Rightarrow (2 n - 4) right ∠s = (12 - 4) right ∠s = 8 right ∠s$

Q13 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

OPEN IN YOUTUBE

Question 13:

Tick (✓) the correct answer:
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°

Answer 13:

(a) 135°

$(2 n - 4) \times 90 = 1080 (2 n - 4) = 12 2 n = 16 o r n = 8 Each interior angle = 180 - \frac{360}{n} = 180 - \frac{360}{8} = 180 - 45 = 135^{o}$

Q14 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

OPEN IN YOUTUBE

Question 14:

Tick (✓) the correct answer:
The interior angle of a regular polygon exceeds its exterior angle by 108°. How many sides does the polygon have?
(a) 16
(b) 14
(c) 12
(d) 10

Answer 14:

(d) 10

$Each exterior angle of a regular polygon = \frac{360}{n} Each interior angle of a regular polygon = 180 - \frac{360}{n} 180 - \frac{360}{n} - 108 = \frac{360}{n} \frac{720}{n} = 180 - 108 = 72 n = \frac{720}{72} = 10$

RS Aggarwal solution class 8 chapter 14 Polygons Exercise 14B

Exercise 14B

Q1 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 1:

Answer 1:

Q2 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 2:

Answer 2:

Q3 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 3:

Answer 3:

Q4 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 4:

Answer 4:

Q5 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 5:

Answer 5:

Page-183

Q6 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 6:

Answer 6:

Q7 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 7:

Answer 7:

Q8 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 8:

Answer 8:

Q9 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 9:

Answer 9:

Q10 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 10:

Answer 10:

Q11 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 11:

Answer 11:

Q12 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 12:

Answer 12:

Q13 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 13:

Answer 13:

Q14 | Ex-14B | Class 8 | RS AGGARWAL | chapter 14 | Polygons

Question 14:

Answer 14:

No comments:

Post a Comment

Contact Form