2. 2
Contents
Chapter 1
Polygons
1. Polygon
2. Examples of polygon
3. Sum of angles
4. Exterior angles
5. Regular polygon
Chapter 2
Rational Numbers
1. Rational Numbers
2. Rational forms
3. Addition and subtraction
4. Multiplication and division
5. Equal fractions
6. Decimal forms
3. 3
Chapter 1
POLYGONS
A polygon is a figure having more than tw sides and angles.
Examples of Polygons
Divide any polygon into another polygon with one side less
and a triangle by drawing a line starting at any vertex,
skipping one vertex and joining with the nest.
4. 4
Sun of the angles
Sum of the angles of a triangle is 1800
Sum of the angles of quadrilateral is 2x1800
Sum of the angles of pentagon is 3 x 1800
The sum of the angles of an n side’s
polygon is (n-2) x 1800
5. 5
Example
A 10 sided polygon has all its angles equal. How much is
each angle?
Number of sides = 10
Sum of the angles = (10-2) x 1800
=14400
External angles
The four external angles and the four angles of the
quadrilateral together make
4 x 1800 = 7200
The sum of the four angles of the quadrilateral is 3600
So, the sum of the four external angle is
7200 – 3600 = 3600
The sum of the external angles
= n x 1800 –[n-2) x 180]
= 2 x 1800
= 3600
6. 6
Example
A 10 sided polygon has all its angles equal. How much is each
external angle?
Since the angles of the polygon are equal. Its external angles
will also be equal.
Sum of the interior angle = 3600
Sum of measure of an external = 3600
10
= 360
RegularPolygon
Polygon with equal angles and equal sides are called regular
polygon.
Example
How much is an internal angle of a 36 regular polygon?
Sum of the external angles = 3600
Measure of an external angle = 3600
36
= 10
The sum of external angles of any
polygon is 3600
7. 7
Measure of an internal angle = 1800 -10
= 1700
Exercise
1. What is the sum of the angles of a polygon with 102 sides?
2. Each external angle of a polygon is 200. How many sides
does it have?
3. Draw a hexagon with all angles equal, but not all sides equal.
8. 8
Chapter 2
RATIONAL NUMBERS
RationalNumber
Integers and fractions are collectively called rational numbers.
Any rational number can be written in the form
𝑥
𝑦
, where x
and y are integers.
Example
1.
𝟏
𝟐
=
𝟐
𝟒
=
𝟑
𝟔
2.
𝟑
𝟓
=
𝟔
𝟏𝟎
=
𝟗
𝟏𝟓
If the numerator and denominator of a rational number
have any common factor then by removing this factor, get
a simpler form of the same rational number.
Example
2x = x
2y y
9. 9
Addition and subtraction
If
𝑎
𝑏
and
𝑝
𝑞
are two rational numbers. Then sum of the
rational number is
𝑎
𝑏
+
𝑝
𝑞
=
𝑎𝑞
𝑏𝑞
+
𝑏𝑝
𝑏𝑞
=
𝑎𝑞+𝑏𝑞
𝑏𝑞
Example
(1) 1 + 1
𝑥
= 𝑥+1
𝑥
If
𝑎
𝑏
and
𝑝
𝑞
are two rational numbers. Then subtraction of
the rational number is
𝑎
𝑏
−
𝑝
𝑞
=
𝑎𝑞
𝑏𝑞
−
𝑏𝑝
𝑏𝑞
=
𝑎𝑞+𝑏𝑞
𝑏𝑞
Example
𝑥
𝑦
−
𝑦
𝑥
=
𝑥2
−𝑦2
𝑥𝑦
10. 10
Multiplication and division
If
𝑎
𝑏
and
𝑝
𝑞
are two rational numbers. Then multiplication of
the rational number is
𝑎
𝑏
×
𝑝
𝑞
=
𝑎𝑝
𝑏𝑞
Example
1.
2
3
×
5
7
=
2×5
3×7
=
10
21
If
𝑎
𝑏
and
𝑝
𝑞
are two rational numbers. Then division of this
rational number is
𝑎
𝑏
÷
𝑝
𝑞
=
𝑎𝑞
𝑏𝑝
Example
𝑥 ÷
𝑢
𝑣
= 𝑥 ×
𝑣
𝑢
=
𝑥𝑣
𝑢
11. 11
Equal Fractions
For the numbers a, b, p, q if
𝑎
𝑏
=
𝑝
𝑞
𝑡hen aq = bp
On the other hand
aq = bp and also b = 0, q = 0 then
𝑎
𝑏
=
𝑝
𝑞
Example
Whether
183
209
𝑎𝑛𝑑
221
247
are equal?
Check whether the product of 187 x 247 and 209 x 221 are equal.
187 x 247 = 46189
209 x 221 = 46189
So,
183
209
𝑎𝑛𝑑
221
247
are equal
For the numbers a, b, b, q if
𝑎
𝑏
=
𝑝
𝑞
then
𝑎
𝑝
=
𝑏
𝑞
Example
x
y
=
2
3
what is
4𝑥+2𝑦
5𝑥−2𝑦
x
y
=
2
3
