Extension - Geometric Patterns

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Copy the table shown at the right. Use the following series of questions to complete the table and discover the geometric pattern that will help you know the sum of the interior angles of any polygon.
1. OK
2. NO
How many angles are in a triangle?
1. 3
Using the concept of diagonals, how many triangles can a triangle be divided into?
1. 1
1 triangle is 180^o.
1. True
2. False
How many angles are in a quadrilateral?
1. 4
Using the concept of diagonals, how many triangles can a quadrilateral be divided into?
1. 2
2 triangles are 180 * 2 = 360^o.
1. True
2. False
How many angles are in a pentagon?
1. 5
Using the concept of diagonals, how many triangles can a pentagon be divided into?
1. 3
3 triangles are 180 * 3 = 540^o.
1. True
2. False
How many angles are in a hexagon?
1. 6
Using the concept of diagonals, how many triangles can a hexagon be divided into?
1. 4
4 triangles are 180 * 4 = 720^o.
1. True
2. False
Complete the table you started in question one.
How many triangles can a heptagon be divided into?
1. 5
What is the sum of the interior angles of a heptagon?
1. 900
2. 180 * 5
What is the sum of the interior angles of an octagon?
1. 1080
2. 180 * 6
What is the sum of the interior angles of an decagon?
1. 1440
2. 180 * 8