Chapter - 14 Polygons | Mathematics (Maths) Class 8 PDF Download

 Page 1


Q u e s t i o n : 1
Find the measure of each exterior angle of a regular
i
pentagon
i i
hexagon
i i i
heptagon
i v
decagon
v
polygon of 15 sides.
S o l u t i o n :
Exterior angle of an n-sided polygon = 
360
n
o
i
For a pentagon: n = 5 ? 
360
n
=
360
5
= 72
o
i i
For a hexagon: n = 6 ? 
360
n
=
360
6
= 60
o
i i i
For a heptagon: n = 7 ? 
360
n
=
360
7
= 51. 43
o
i v
For a decagon: n = 10 ? 
360
n
=
360
10
= 36
o
v
For a polygon of 15 sides: n = 15 ? 
360
n
=
360
15
= 24
o
Q u e s t i o n : 2
Is it possible to have a regular polygon each of whose exterior angles is 50°?
S o l u t i o n :
Each exterior angle of an n-sided polygon = 
360
n
o
If the exterior angle is 50°, then:
 
360
n
= 50 ? n = 7. 2
Since n is not an integer, we cannot have a polygon with each exterior angle equal to 50°.
Q u e s t i o n : 3
Find the measure of each interior angle of a regular polygon having
i
10 sides
i i
15 sides.
S o l u t i o n :
For a regular polygon with n sides:
Each interior angle = 180 - {Each exterior angle} = 180 -
360
n
i
For a polygon with 10 sides:
  Each exterior angle = 
360
10
= 36
o
? Each interior angle = 180 -36 = 144
o
i i
For a polygon with 15 sides:
   Each exterior angle = 
360
15
= 24
o
? Each interior angle = 180 -24 = 156
o
Q u e s t i o n : 4
Is it possible to have a regular polygon each of whose interior angles is 100°?
S o l u t i o n :
( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )
( )
( )
Page 2


Q u e s t i o n : 1
Find the measure of each exterior angle of a regular
i
pentagon
i i
hexagon
i i i
heptagon
i v
decagon
v
polygon of 15 sides.
S o l u t i o n :
Exterior angle of an n-sided polygon = 
360
n
o
i
For a pentagon: n = 5 ? 
360
n
=
360
5
= 72
o
i i
For a hexagon: n = 6 ? 
360
n
=
360
6
= 60
o
i i i
For a heptagon: n = 7 ? 
360
n
=
360
7
= 51. 43
o
i v
For a decagon: n = 10 ? 
360
n
=
360
10
= 36
o
v
For a polygon of 15 sides: n = 15 ? 
360
n
=
360
15
= 24
o
Q u e s t i o n : 2
Is it possible to have a regular polygon each of whose exterior angles is 50°?
S o l u t i o n :
Each exterior angle of an n-sided polygon = 
360
n
o
If the exterior angle is 50°, then:
 
360
n
= 50 ? n = 7. 2
Since n is not an integer, we cannot have a polygon with each exterior angle equal to 50°.
Q u e s t i o n : 3
Find the measure of each interior angle of a regular polygon having
i
10 sides
i i
15 sides.
S o l u t i o n :
For a regular polygon with n sides:
Each interior angle = 180 - {Each exterior angle} = 180 -
360
n
i
For a polygon with 10 sides:
  Each exterior angle = 
360
10
= 36
o
? Each interior angle = 180 -36 = 144
o
i i
For a polygon with 15 sides:
   Each exterior angle = 
360
15
= 24
o
? Each interior angle = 180 -24 = 156
o
Q u e s t i o n : 4
Is it possible to have a regular polygon each of whose interior angles is 100°?
S o l u t i o n :
( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )
( )
( )
Each interior angle of a regular polygon having n sides = 180 - 
360
n
=
180 n-360
n
If each interior angle of the polygon is 100°, then:
100 =
180 n-360
n
? 100 n = 180 n - 360 ? 180 n -100 n = 360 ?  80 n = 360 ?  n =
360
80
= 4. 5
Since n is not an integer, it is not possible to have a regular polygon with each interior angle equal to 100°.
Q u e s t i o n : 5
What is the sum of all interior angles of a regular
i
pentagon
i i
hexagon
i i i
nonagon
i v
polygon of 12 sides?
S o l u t i o n :
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°
i i
For a hexagon:
 n = 6 ? ( n -2)×180° = (6 -2)×180° = 4 ×180° = 720°
i i i
For a nonagon:
n = 9 ? ( n -2)×180° = (9 -2)×180° = 7 ×180° = 1260°
i v
For a polygon of 12 sides:
n = 12 ? ( n -2)×180° = (12 -2)×180° = 10 ×180° = 1800°
Q u e s t i o n : 6
What is the number of diagonals in a
i
heptagon
i i
octagon
i i i
polygon of 12 sides?
S o l u t i o n :
Number of diagonal in an n-sided polygon = 
n( n-3)
2
i
For a heptagon:
 n = 7 ?
n( n-3)
2
=
7(7-3)
2
=
28
2
= 14
i i
For an octagon:
 n = 8 ?
n( n-3)
2
=
8(8-3)
2
=
40
2
= 20
i i i
For a 12-sided polygon:
 n = 12 ?
n( n-3)
2
=
12(12-3)
2
=
108
2
= 54
Q u e s t i o n : 7
Find the number of sides of a regular polygon whose each exterior angle measures:
i
40°
i i
36°
i i i
72°
i v
30°
S o l u t i o n :
Sum of all the exterior angles of a regular polygon is 360
o
?.
i
( )
Page 3


Q u e s t i o n : 1
Find the measure of each exterior angle of a regular
i
pentagon
i i
hexagon
i i i
heptagon
i v
decagon
v
polygon of 15 sides.
S o l u t i o n :
Exterior angle of an n-sided polygon = 
360
n
o
i
For a pentagon: n = 5 ? 
360
n
=
360
5
= 72
o
i i
For a hexagon: n = 6 ? 
360
n
=
360
6
= 60
o
i i i
For a heptagon: n = 7 ? 
360
n
=
360
7
= 51. 43
o
i v
For a decagon: n = 10 ? 
360
n
=
360
10
= 36
o
v
For a polygon of 15 sides: n = 15 ? 
360
n
=
360
15
= 24
o
Q u e s t i o n : 2
Is it possible to have a regular polygon each of whose exterior angles is 50°?
S o l u t i o n :
Each exterior angle of an n-sided polygon = 
360
n
o
If the exterior angle is 50°, then:
 
360
n
= 50 ? n = 7. 2
Since n is not an integer, we cannot have a polygon with each exterior angle equal to 50°.
Q u e s t i o n : 3
Find the measure of each interior angle of a regular polygon having
i
10 sides
i i
15 sides.
S o l u t i o n :
For a regular polygon with n sides:
Each interior angle = 180 - {Each exterior angle} = 180 -
360
n
i
For a polygon with 10 sides:
  Each exterior angle = 
360
10
= 36
o
? Each interior angle = 180 -36 = 144
o
i i
For a polygon with 15 sides:
   Each exterior angle = 
360
15
= 24
o
? Each interior angle = 180 -24 = 156
o
Q u e s t i o n : 4
Is it possible to have a regular polygon each of whose interior angles is 100°?
S o l u t i o n :
( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )
( )
( )
Each interior angle of a regular polygon having n sides = 180 - 
360
n
=
180 n-360
n
If each interior angle of the polygon is 100°, then:
100 =
180 n-360
n
? 100 n = 180 n - 360 ? 180 n -100 n = 360 ?  80 n = 360 ?  n =
360
80
= 4. 5
Since n is not an integer, it is not possible to have a regular polygon with each interior angle equal to 100°.
Q u e s t i o n : 5
What is the sum of all interior angles of a regular
i
pentagon
i i
hexagon
i i i
nonagon
i v
polygon of 12 sides?
S o l u t i o n :
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°
i i
For a hexagon:
 n = 6 ? ( n -2)×180° = (6 -2)×180° = 4 ×180° = 720°
i i i
For a nonagon:
n = 9 ? ( n -2)×180° = (9 -2)×180° = 7 ×180° = 1260°
i v
For a polygon of 12 sides:
n = 12 ? ( n -2)×180° = (12 -2)×180° = 10 ×180° = 1800°
Q u e s t i o n : 6
What is the number of diagonals in a
i
heptagon
i i
octagon
i i i
polygon of 12 sides?
S o l u t i o n :
Number of diagonal in an n-sided polygon = 
n( n-3)
2
i
For a heptagon:
 n = 7 ?
n( n-3)
2
=
7(7-3)
2
=
28
2
= 14
i i
For an octagon:
 n = 8 ?
n( n-3)
2
=
8(8-3)
2
=
40
2
= 20
i i i
For a 12-sided polygon:
 n = 12 ?
n( n-3)
2
=
12(12-3)
2
=
108
2
= 54
Q u e s t i o n : 7
Find the number of sides of a regular polygon whose each exterior angle measures:
i
40°
i i
36°
i i i
72°
i v
30°
S o l u t i o n :
Sum of all the exterior angles of a regular polygon is 360
o
?.
i
( )
Each exterior angle = 40
o
Number of sides of the regular polygon = 
360
40
= 9
i i
Each exterior angle = 36
o
Number of sides of the regular polygon = 
360
36
= 10
i i i
Each exterior angle = 72
o
Number of sides of the regular polygon = 
360
72
= 5
i v
Each exterior angle = 30
o
Number of sides of the regular polygon = 
360
30
= 12
Q u e s t i o n : 8
In the given figure, find the angle measure x.
S o l u t i o n :
Sum of all the interior angles of an n-sided polygon = ( n -2)×180°
m ? A D C = 180 -50 = 130
o
m ? D A B = 180 -115 = 65
o
m ? B C D = 180 -90 = 90
o
 m ? A D C + m ? D A B + m ? B C D + m ? A B C = ( n -2)×180° = 4 -2 ×180° = 2 ×180° = 360° ?  m ? A D C + m ? D A B
? x = 105
Q u e s t i o n : 9
Find the angle measure x in the given figure.
S o l u t i o n :
For a regular n-sided polygon:
Each interior angle = 180 -
360
n
In the given figure:
   n = 5 x° = 180 -
360
5
     = 180 -72     = 108
o
? x = 108
Q u e s t i o n : 1 0
Tick
? the correct answer:
How many diagonals are there in a pentagon?
a
5
b
7
c
6
d
10
S o l u t i o n :
a
5
For a pentagon:
n = 5
Number of diagonals = 
n( n-3)
2
=
5(5-3)
2
= 5
Q u e s t i o n : 1 1
Tick
? the correct answer:
How many diagonals are there in a hexagon?
a
6
b
( )
( )
Page 4


Q u e s t i o n : 1
Find the measure of each exterior angle of a regular
i
pentagon
i i
hexagon
i i i
heptagon
i v
decagon
v
polygon of 15 sides.
S o l u t i o n :
Exterior angle of an n-sided polygon = 
360
n
o
i
For a pentagon: n = 5 ? 
360
n
=
360
5
= 72
o
i i
For a hexagon: n = 6 ? 
360
n
=
360
6
= 60
o
i i i
For a heptagon: n = 7 ? 
360
n
=
360
7
= 51. 43
o
i v
For a decagon: n = 10 ? 
360
n
=
360
10
= 36
o
v
For a polygon of 15 sides: n = 15 ? 
360
n
=
360
15
= 24
o
Q u e s t i o n : 2
Is it possible to have a regular polygon each of whose exterior angles is 50°?
S o l u t i o n :
Each exterior angle of an n-sided polygon = 
360
n
o
If the exterior angle is 50°, then:
 
360
n
= 50 ? n = 7. 2
Since n is not an integer, we cannot have a polygon with each exterior angle equal to 50°.
Q u e s t i o n : 3
Find the measure of each interior angle of a regular polygon having
i
10 sides
i i
15 sides.
S o l u t i o n :
For a regular polygon with n sides:
Each interior angle = 180 - {Each exterior angle} = 180 -
360
n
i
For a polygon with 10 sides:
  Each exterior angle = 
360
10
= 36
o
? Each interior angle = 180 -36 = 144
o
i i
For a polygon with 15 sides:
   Each exterior angle = 
360
15
= 24
o
? Each interior angle = 180 -24 = 156
o
Q u e s t i o n : 4
Is it possible to have a regular polygon each of whose interior angles is 100°?
S o l u t i o n :
( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )
( )
( )
Each interior angle of a regular polygon having n sides = 180 - 
360
n
=
180 n-360
n
If each interior angle of the polygon is 100°, then:
100 =
180 n-360
n
? 100 n = 180 n - 360 ? 180 n -100 n = 360 ?  80 n = 360 ?  n =
360
80
= 4. 5
Since n is not an integer, it is not possible to have a regular polygon with each interior angle equal to 100°.
Q u e s t i o n : 5
What is the sum of all interior angles of a regular
i
pentagon
i i
hexagon
i i i
nonagon
i v
polygon of 12 sides?
S o l u t i o n :
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°
i i
For a hexagon:
 n = 6 ? ( n -2)×180° = (6 -2)×180° = 4 ×180° = 720°
i i i
For a nonagon:
n = 9 ? ( n -2)×180° = (9 -2)×180° = 7 ×180° = 1260°
i v
For a polygon of 12 sides:
n = 12 ? ( n -2)×180° = (12 -2)×180° = 10 ×180° = 1800°
Q u e s t i o n : 6
What is the number of diagonals in a
i
heptagon
i i
octagon
i i i
polygon of 12 sides?
S o l u t i o n :
Number of diagonal in an n-sided polygon = 
n( n-3)
2
i
For a heptagon:
 n = 7 ?
n( n-3)
2
=
7(7-3)
2
=
28
2
= 14
i i
For an octagon:
 n = 8 ?
n( n-3)
2
=
8(8-3)
2
=
40
2
= 20
i i i
For a 12-sided polygon:
 n = 12 ?
n( n-3)
2
=
12(12-3)
2
=
108
2
= 54
Q u e s t i o n : 7
Find the number of sides of a regular polygon whose each exterior angle measures:
i
40°
i i
36°
i i i
72°
i v
30°
S o l u t i o n :
Sum of all the exterior angles of a regular polygon is 360
o
?.
i
( )
Each exterior angle = 40
o
Number of sides of the regular polygon = 
360
40
= 9
i i
Each exterior angle = 36
o
Number of sides of the regular polygon = 
360
36
= 10
i i i
Each exterior angle = 72
o
Number of sides of the regular polygon = 
360
72
= 5
i v
Each exterior angle = 30
o
Number of sides of the regular polygon = 
360
30
= 12
Q u e s t i o n : 8
In the given figure, find the angle measure x.
S o l u t i o n :
Sum of all the interior angles of an n-sided polygon = ( n -2)×180°
m ? A D C = 180 -50 = 130
o
m ? D A B = 180 -115 = 65
o
m ? B C D = 180 -90 = 90
o
 m ? A D C + m ? D A B + m ? B C D + m ? A B C = ( n -2)×180° = 4 -2 ×180° = 2 ×180° = 360° ?  m ? A D C + m ? D A B
? x = 105
Q u e s t i o n : 9
Find the angle measure x in the given figure.
S o l u t i o n :
For a regular n-sided polygon:
Each interior angle = 180 -
360
n
In the given figure:
   n = 5 x° = 180 -
360
5
     = 180 -72     = 108
o
? x = 108
Q u e s t i o n : 1 0
Tick
? the correct answer:
How many diagonals are there in a pentagon?
a
5
b
7
c
6
d
10
S o l u t i o n :
a
5
For a pentagon:
n = 5
Number of diagonals = 
n( n-3)
2
=
5(5-3)
2
= 5
Q u e s t i o n : 1 1
Tick
? the correct answer:
How many diagonals are there in a hexagon?
a
6
b
( )
( )
8
c
9
d
10
S o l u t i o n :
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
                    =
18
2
= 9
Q u e s t i o n : 1 2
Tick
? the correct answer:
How many diagonals are there in an octagon?
a
8
b
16
c
18
d
20
S o l u t i o n :
d
20
?For a regular n-sided polygon:
Number of diagonals =: 
n( n-3)
2
For an octagon:
 n = 8
8(8-3)
2
=
40
2
= 20
Q u e s t i o n : 1 3
Tick
? the correct answer:
How many diagonals are there in a polygon having 12 sides?
a
12
b
24
c
36
d
54
S o l u t i o n :
d
54
For an n-sided polygon:
Number of diagonals = 
n( n-3)
2
? n = 12 ?
12(12-3)
2
= 54
Q u e s t i o n : 1 4
Tick
? the correct answer:
A polygon has 27 diagonals. How many sides does it have?
a
7
b
8
c
9
d
12
S o l u t i o n :
c
9
n( n-3)
2
= 27 ? n( n -3) = 54 ? n
2
-3 n -54 = 0 ? n
2
-9 n +6 n -54 = 0 ? n( n -9)+6( n -9) = 0 ? n = -6 o r n = 9Number of sides cannot be negative. ? n = 9
Q u e s t i o n : 1 5
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
Page 5


Q u e s t i o n : 1
Find the measure of each exterior angle of a regular
i
pentagon
i i
hexagon
i i i
heptagon
i v
decagon
v
polygon of 15 sides.
S o l u t i o n :
Exterior angle of an n-sided polygon = 
360
n
o
i
For a pentagon: n = 5 ? 
360
n
=
360
5
= 72
o
i i
For a hexagon: n = 6 ? 
360
n
=
360
6
= 60
o
i i i
For a heptagon: n = 7 ? 
360
n
=
360
7
= 51. 43
o
i v
For a decagon: n = 10 ? 
360
n
=
360
10
= 36
o
v
For a polygon of 15 sides: n = 15 ? 
360
n
=
360
15
= 24
o
Q u e s t i o n : 2
Is it possible to have a regular polygon each of whose exterior angles is 50°?
S o l u t i o n :
Each exterior angle of an n-sided polygon = 
360
n
o
If the exterior angle is 50°, then:
 
360
n
= 50 ? n = 7. 2
Since n is not an integer, we cannot have a polygon with each exterior angle equal to 50°.
Q u e s t i o n : 3
Find the measure of each interior angle of a regular polygon having
i
10 sides
i i
15 sides.
S o l u t i o n :
For a regular polygon with n sides:
Each interior angle = 180 - {Each exterior angle} = 180 -
360
n
i
For a polygon with 10 sides:
  Each exterior angle = 
360
10
= 36
o
? Each interior angle = 180 -36 = 144
o
i i
For a polygon with 15 sides:
   Each exterior angle = 
360
15
= 24
o
? Each interior angle = 180 -24 = 156
o
Q u e s t i o n : 4
Is it possible to have a regular polygon each of whose interior angles is 100°?
S o l u t i o n :
( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )
( )
( )
Each interior angle of a regular polygon having n sides = 180 - 
360
n
=
180 n-360
n
If each interior angle of the polygon is 100°, then:
100 =
180 n-360
n
? 100 n = 180 n - 360 ? 180 n -100 n = 360 ?  80 n = 360 ?  n =
360
80
= 4. 5
Since n is not an integer, it is not possible to have a regular polygon with each interior angle equal to 100°.
Q u e s t i o n : 5
What is the sum of all interior angles of a regular
i
pentagon
i i
hexagon
i i i
nonagon
i v
polygon of 12 sides?
S o l u t i o n :
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°
i i
For a hexagon:
 n = 6 ? ( n -2)×180° = (6 -2)×180° = 4 ×180° = 720°
i i i
For a nonagon:
n = 9 ? ( n -2)×180° = (9 -2)×180° = 7 ×180° = 1260°
i v
For a polygon of 12 sides:
n = 12 ? ( n -2)×180° = (12 -2)×180° = 10 ×180° = 1800°
Q u e s t i o n : 6
What is the number of diagonals in a
i
heptagon
i i
octagon
i i i
polygon of 12 sides?
S o l u t i o n :
Number of diagonal in an n-sided polygon = 
n( n-3)
2
i
For a heptagon:
 n = 7 ?
n( n-3)
2
=
7(7-3)
2
=
28
2
= 14
i i
For an octagon:
 n = 8 ?
n( n-3)
2
=
8(8-3)
2
=
40
2
= 20
i i i
For a 12-sided polygon:
 n = 12 ?
n( n-3)
2
=
12(12-3)
2
=
108
2
= 54
Q u e s t i o n : 7
Find the number of sides of a regular polygon whose each exterior angle measures:
i
40°
i i
36°
i i i
72°
i v
30°
S o l u t i o n :
Sum of all the exterior angles of a regular polygon is 360
o
?.
i
( )
Each exterior angle = 40
o
Number of sides of the regular polygon = 
360
40
= 9
i i
Each exterior angle = 36
o
Number of sides of the regular polygon = 
360
36
= 10
i i i
Each exterior angle = 72
o
Number of sides of the regular polygon = 
360
72
= 5
i v
Each exterior angle = 30
o
Number of sides of the regular polygon = 
360
30
= 12
Q u e s t i o n : 8
In the given figure, find the angle measure x.
S o l u t i o n :
Sum of all the interior angles of an n-sided polygon = ( n -2)×180°
m ? A D C = 180 -50 = 130
o
m ? D A B = 180 -115 = 65
o
m ? B C D = 180 -90 = 90
o
 m ? A D C + m ? D A B + m ? B C D + m ? A B C = ( n -2)×180° = 4 -2 ×180° = 2 ×180° = 360° ?  m ? A D C + m ? D A B
? x = 105
Q u e s t i o n : 9
Find the angle measure x in the given figure.
S o l u t i o n :
For a regular n-sided polygon:
Each interior angle = 180 -
360
n
In the given figure:
   n = 5 x° = 180 -
360
5
     = 180 -72     = 108
o
? x = 108
Q u e s t i o n : 1 0
Tick
? the correct answer:
How many diagonals are there in a pentagon?
a
5
b
7
c
6
d
10
S o l u t i o n :
a
5
For a pentagon:
n = 5
Number of diagonals = 
n( n-3)
2
=
5(5-3)
2
= 5
Q u e s t i o n : 1 1
Tick
? the correct answer:
How many diagonals are there in a hexagon?
a
6
b
( )
( )
8
c
9
d
10
S o l u t i o n :
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
                    =
18
2
= 9
Q u e s t i o n : 1 2
Tick
? the correct answer:
How many diagonals are there in an octagon?
a
8
b
16
c
18
d
20
S o l u t i o n :
d
20
?For a regular n-sided polygon:
Number of diagonals =: 
n( n-3)
2
For an octagon:
 n = 8
8(8-3)
2
=
40
2
= 20
Q u e s t i o n : 1 3
Tick
? the correct answer:
How many diagonals are there in a polygon having 12 sides?
a
12
b
24
c
36
d
54
S o l u t i o n :
d
54
For an n-sided polygon:
Number of diagonals = 
n( n-3)
2
? n = 12 ?
12(12-3)
2
= 54
Q u e s t i o n : 1 4
Tick
? the correct answer:
A polygon has 27 diagonals. How many sides does it have?
a
7
b
8
c
9
d
12
S o l u t i o n :
c
9
n( n-3)
2
= 27 ? n( n -3) = 54 ? n
2
-3 n -54 = 0 ? n
2
-9 n +6 n -54 = 0 ? n( n -9)+6( n -9) = 0 ? n = -6 o r n = 9Number of sides cannot be negative. ? n = 9
Q u e s t i o n : 1 5
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°
S o l u t i o n :
b
68°
?Sum of all the interior angles of a polygon with n sides = ( n -2)×180°
? 5 -2 ×180
o
= x + x +20 + x +40 + x +60 + x +80 ? 540 = 5 x + 200 ? 5 x = 340 ? x = 68
o
Q u e s t i o n : 1 6
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
S o l u t i o n :
b
9
Each exterior angle of a regular n -sided polygon = 
360
n
= 40                                                           ? n =
360
40
= 9
Q u e s t i o n : 1 7
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
S o l u t i o n :
c
5
?Each interior angle for a regular n-sided polygon = 180 -
360
n
180 -
360
n
= 108 ? 
360
n
= 72 ? n =
360
72
= 5
Q u e s t i o n : 1 8
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
S o l u t i o n :
a
8
Each interior angle of a regular polygon with n sides = 180 - 
360
n
?  180 - 
360
n
= 135 ? 
360
n
= 45 ? n = 8
Q u e s t i o n : 1 9
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
S o l u t i o n :
b
8
For a regular polygon with n sides:
Each exterior angle = 
360
n
( )
( )
( ) ( )
( ) ( )