Back to: MATHEMATICS JSS 2
Welcome to JSS2 Third Term!
We are eager to have you join us in class!!
In today’s Mathematics class, We will be discussing Angles and Polygons. We hope you enjoy the class!
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 a straight side. A regular polygon has all sides and angles equal.
Polygons are named according to the number of sides they have. Examples are:
Triangle a 3 sided polygon
Quadrilateral a 4 sided polygon
Pentagon a 5 sided polygon
Hexagon a 6 sided polygon
Heptagon a 7 sided polygon
Octagon an 8 sided polygon
Nonagon a 9 sided polygon
Decagon a 10 sided polygon
The diagrams below represent some common polygons.
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:
The number of triangles depends on the number of sides of the polygon. For a polygon with ‘n’ sides, there will be (n2) triangles. The sum of angles of a triangle is 180^{0}.
Alternatively, since 180^{0} = (n2) x 2 x 90
= 2(n2) 90
= (2n4) 90
Thus, the sum of the angles of an nsided polygon can be represented as (n2) 180^{0} or (2n4) 90^{0}
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
(n2) 
Sum of interior Angles (n2) 180^{0} 
Triangle  3  3 – 2 = 1  1 x 180^{0} = 180 
Quadrilateral  4  4 – 2 = 2  2 x 180^{0} = 360^{0} 
Pentagon  5  5 – 2 = 3  3 x 180^{0} = 540^{0} 
Hexagon  6  6 – 2 = 4  4 x 180^{0} = 720^{0} 
Heptagon  7  7 – 2 = 5  5 x 180^{0} = 900^{0} 
Octagon  8  8 – 2 = 6  6 x 180^{0} = 1080^{0} 
Nonagon  9  9 – 2 = 7  7 x 180^{0} = 1260^{0} 
Decagon  10  10 – 2 = 8  8 x 180^{0} = 1440^{0} 
Worked Examples:
 Calculate the size of an exterior angle of a regular nonagon (9 sides)
 Calculate the size of an exterior angle of a regular hexagon (6 sides)
Answer to the evaluation questions
 Sum of the exterior of a polygon = 360^{0}. Number of sides of a nonagon = 9
$Sizeofeachexteriorangle=\frac{sumofexteriorangles/number}{numbweofsides}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}=\frac{{360}^{o}}{9}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}={40}^{o}$
 Sum of exterior angles = 360^{o}
Hexagon has 6 sides.
= 60^{o}
GENERAL EVALUATION
 The interior angles of a triangle add up to …………………………
 The interior angles of a quadrilateral add up to ………………………
 The sum of the interior angles of a regular polygon is 1080^{o}. How many sides has the polygon?
REVISION QUESTION
 Calculate the number of sides of each of a regular polygon whose interior angle is 162^{o}
 The sum of the 3 angles of a hexagon is 345^{o}. If the other angles are equal. Find the sizes of each of the angle.
READING ASSIGNMENT
Essential Mathematics for junior secondary school Book 2, Chapter 19, page 252 – 255
Exercise 19.5 No 1 page 255
WEEKEND ASSIGNMENT
 The sum of the interior angles of a regular pentagon is A. 240^{o} B. 720^{o} C. 540^{o} D. 640^{o}
 Calculate the size of each exterior angle of a regular hexagon. A. 60^{o} B. 30^{o} C. 45^{o} D. 125^{o}
 The size of each angle of a regular octagon will be ____ A. 95^{o} B. 75^{o} C. 105^{o} D. 135^{o}
 How many sides has a polygon if the sum of interior angles of that polygon gives 3240^{o}? A. 18^{o} B. 15^{o} C. 17^{o} D. 20^{o}
 Calculate the size of each exterior angles of a pentagon A. 30^{o} B. 72^{o} C. 60^{o} D. 90^{o}
THEORY
 Calculate

 A. The total internal angels of an octagon
 B. The size of each angle of a regular octagon

 Calculate the

 Exterior angle
 The number of sides of a regular polygon with an interior angle of 72^{o}

We have come to the end of this class. We do hope you enjoyed the class?
Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.
In our next class, we will be talking about “Angles of Elevation and Depression”. We are very much eager to meet you there.
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