# Lesson Notes By Weeks and Term - Junior Secondary School 2

ANGLES IN POLYGON

SUBJECT: MATHEMATICS

CLASS:  JSS 2

DATE:

TERM: 3rd TERM

REFERENCE

• WABP ESSENTIAL MATHEMATICS FOR JSS BK 2 BY A.J.S. OLUWASANMI
• NEW GENERAL MATHEMATICS BY J.B. CHANNON & ETAL

WEEK TWO

TOPIC: ANGLES IN POLYGON

CONTENT:    (i) Sum of interior angles of a polygon

(ii) Sum of exterior angles of a polygon

DEFINITION OF A POLYGON

A polygon is any close plane figure with straight side. A regular polygon has all sides and angles equal.

Polygon are named according to the number of sides they have. Examples are:

Triangle         a 3- sided polygon

Pentagon        a 5- sided polygon

Hexagon        a 6- sided polygon

Heptagon        a 7- sided polygon

Octagon        a 8- sided polygon

Nonagon        a 9- sided polygon

Decagon        a 10- sided polygon

The diagrams below represent some common polygons.

(3 sided)            (4- sided)            (5- sided)        (6- sided)

Reference

NGM Book 2

Essential Mathematics for junior secondary school Book 2, chapter 9, pages 87 – 88

Sum of Interior Angles of a Polygon

The angles inside a polygon are called its interior angles as shown in the figure below:

e = exterior angle

i = interior angle

The number of triangles depends on the number of sides of the polygon. For a polygon with ‘n’ sides there will be (n-2) triangles. The sum of angles of a triangle is 1800.

Alternatively, since 1800 = (n-2) x 2 x 90

= 2(n-2) 90

= (2n-4) 90

Thus, the sum of the angles of an n-sided polygon can be represented as (n-2) 1800 or (2n-4) 900

The table below shows the sum of interior angles of a regular polygon of a 3 sided polygon up to a sided polygon.

 Polygon No. of Sides No. of Triangles (n-2) Sum of interior Angles (n-2) 1800 Triangle 3 3 – 2 = 1 1 x 1800 = 180 Quadrilateral 4 4 – 2 = 2 2 x 1800 = 3600 Pentagon 5 5 – 2 = 3 3 x 1800 = 5400 Hexagon 6 6 – 2 = 4 4 x 1800 = 7200 Heptagon 7 7 – 2 = 5 5 x 1800 = 9000 Octagon 8 8 – 2 = 6 6 x 1800 = 10800 Nonagon 9 9 – 2 = 7 7 x 1800 = 12600 Decagon 10 10 – 2 = 8 8 x 1800 = 14400

Worked Examples:

1. Calculate the size of exterior angle of a regular nonagon (9 sides)
2. Calculate the size of exterior angle of a regular hexagon (6 sides)

1. Sum of exterior of a polygon = 3600. Number of sides of a nonagon = 9

Size of each exterior angle = sum of exterior angles/number of sides.

= 360°9

= 40o

1. Sum of exterior angles = 360o

Hexagon has 6 sides.

Size of each exterior angle = sum of exterior anlgesno of sides

= 360°6=60o

GENERAL EVALUATION

1. The interior angles of a triangle add up to …………………………
3. The sum of the interior angles of a regular polygon is 1080o. How many sides has the polygon?

REVISION QUESTION

1. Calculate the number of sides of each of a regular polygon whose interior angle is 162o
2. The sum of the 3 angles of a hexagon is 345o. If the other angles are equal. Find the sizes of each of the angle.

Essential Mathematics for junior secondary school Book 2, Chapter 19, page 252 - 255

Exercise 19.5 No 1 page 255

WEEKEND ASSIGNMENT

1. The sum of interior for angle of a regular pentagon is   A. 240o      B. 720o    C. 540o     D. 640o
2. Calculate the size of each of exterior angle of a regular hexagon.   A. 60o    B. 30o     C. 45o     D. 125o
3. The size of each angle of a regular octagon will be ____ A. 95o     B. 75o     C. 105o     D. 135o
4. How many sides has a polygon if the sum of interior angles of that polygon gives 3240o?     A. 18o      B. 15o      C. 17o     D. 20o
5. Calculate the size of each exterior angles of a pentagon     A. 30o     B, 72o      C. 60o     D. 90o

THEORY

1. Calculate A. The total internal angels of an octagon B. The size of each angle of a regular octagon
2. Calculate the
1. Exterior angle
2. The number of sides of a regular polygon with an interior angle of 72o