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 = n(n-3)2=5(5-3)2=5
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 = n(n-3)2
For a hexagon:
n=6∴ n(n-3)2=6(6-3)2 =182=9
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 =: n(n-3)2
For an octagon:
n=88(8-3)2=402=20
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 = n(n-3)2
∴ n=12⇒12(12-3)2=54
Question 5:
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A polygon has 27 diagonals. How many sides does it have?
(a) 7
(b) 8
(c) 9
(d) 12
Answer 5:
(c) 9
n(n-3)2=27⇒ n(n-3)=54⇒ n2-3n-54 = 0⇒ n2-9n+6n-54=0⇒ n(n-9)+6(n-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=3(360n)⇒ 180 = 4(360n)⇒ 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=1080(2n-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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