Showing posts with label Polygons. Show all posts
Showing posts with label Polygons. Show all posts

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 = nn-32=55-32=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 = nn-32
For a hexagon:

n=6∴ nn-32=66-32                    =182=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 =: nn-32
For an octagon:

 n=888-32=402=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 = nn-32

∴ n=12⇒1212-32=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

nn-32=27⇒ nn-3=54⇒ n2-3n-54 = 0⇒ n2-9n+6n-54=0⇒ nn-9+6n-9=0⇒ n=-6 or n=9Number of sides cannot be negative. ∴n =9


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

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-2×180°

∴(5-2)×180°=x+x+20+x+40+x+60+x+80⇒ 540 = 5x + 200⇒ 5x = 340⇒ x = 68°


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

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 = 360n=40                                                           ⇒n=36040=9


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

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 = 180-360n

180-360n=108⇒ 360n=72⇒ n=36072=5


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

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 - 360n⇒  180 - 360n=135⇒ 360n=45⇒ n= 8


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

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 = 360n
Each interior angle = 180-360n

∴180-360n=3360n⇒ 180 = 4360n⇒ n=4×360180=8


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

Question 11:

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

Answer 11:

(c) 144°
Each interior angle of a regular decagon = 180-36010=180-36=144o


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

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 right ∠s
Sum of all the interior angles of a hexagon is 2n-4 right angles.
For a hexagon:
n=6 ⇒2n-4 right ∠s=12-4 right ∠s=8 right ∠s


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

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°

2n-4×90=10802n-4=122n=16or n=8Each interior angle = 180 - 360n=180 - 3608=180 - 45 =135o


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

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 = 360nEach interior angle of a regular polygon = 180-360n180-360n-108 =360n720n=180-108=72n=72072=10

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RS Aggarwal solution class 8 chapter 14 Polygons Exercise 14A

Exercise 14A

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

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.

Answer 1:

Exterior angle of an n-sided polygon = 360no
(i) For a pentagon: n=5 ∴ 360n=3605=72o

(ii) For a hexagon: n=6 ∴ 360n=3606=60o

(iii) For a heptagon: n=7 ∴ 360n=3607=51.43o

(iv) For a decagon: n=10 ∴ 360n=36010=36o

(v) For a polygon of 15 sides: n=15 ∴ 360n=36015=24o


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

Question 2:

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

Answer 2:

Each exterior angle of an n-sided polygon = 360no
If the exterior angle is 50°, then:

 360n=50⇒n=7.2

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


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

Question 3:

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

Answer 3:

For a regular polygon with n sides:
Each interior angle = 180 - Each exterior angle=180-360n

(i) For a polygon with 10 sides:
  Each exterior angle = 36010=36o⇒ Each interior angle = 180-36=144o

(ii) For a polygon with 15 sides:
   Each exterior angle = 36015=24o⇒ Each interior angle = 180-24=156o


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

Question 4:

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

Answer 4:

Each interior angle of a regular polygon having n sides = 180 - 360n=180n-360n

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

100 =180n-360n⇒ 100n = 180n - 360⇒ 180n-100n=360⇒  80n=360⇒  n=36080=4.5

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


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

Question 5:

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

Answer 5:

Sum of the interior angles of an n-sided polygon = n-2×180°

(i) For a pentagon:
n=5∴ n-2×180°=5-2×180°=3×180° = 540°

(ii) For a hexagon:
 n=6∴ n-2×180°=6-2×180°=4×180° = 720°

(iii) For a nonagon:
n=9∴ n-2×180°=9-2×180°=7×180° = 1260°

(iv) For a polygon of 12 sides:
n=12∴ n-2×180°=12-2×180°=10×180° = 1800°


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

Question 6:

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

Answer 6:

Number of diagonal in an n-sided polygon = nn-32
(i) For a heptagon:

 n=7⇒nn-32=77-32=282=14

(ii) For an octagon:

 n=8⇒nn-32=88-32=402=20

(iii) For a 12-sided polygon:

 n=12⇒nn-32=1212-32=1082=54


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

Question 7:

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

Answer 7:

Sum of all the exterior angles of a regular polygon is 360o​.

(i)
Each exterior angle=40oNumber of sides of the regular polygon = 36040=9

(ii)
Each exterior angle=36oNumber of sides of the regular polygon= 36036=10

(iii)
Each exterior angle=72oNumber of sides of the regular polygon = 36072=5

(iv)
Each exterior angle=30oNumber of sides of the regular polygon = 36030=12


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

Question 8:

In the given figure, find the angle measure x.







Answer 8:

Sum of all the interior angles of an n-sided polygon = n-2×180°

m∠ADC=180-50=130om∠DAB=180-115 =65om∠BCD=180-90=90o m∠ADC+m∠DAB+m∠BCD+m∠ABC=n-2×180°=(4-2)×180°=2×180°=360°⇒  m∠ADC+m∠DAB+m∠BCD+m∠ABC = 360°⇒ 130o + 65o + 90o + m∠ABC = 360°⇒ 285o+m∠ABC=360o⇒ m∠ABC=75o⇒ m∠CBF = 180 - 75 = 105o
∴ x = 105


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

Question 9:

Find the angle measure x in the given figure.









Answer 9:

For a regular n-sided polygon:
Each interior angle = 180-360n
In the given figure:
   n=5 x° = 180-3605     =180-72     =108o
∴ x = 108

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