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Investigation: Total Interior Angle in a Polygon

Last updated almost 3 years ago

16 questions

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Question 16

16.

What connection can you see between the number of triangles, the number of sides of a polygon and the total interior angle? Can you write the relationship as an equation?

In this exercise, you will figure out a general rule to describe the sum of internal angles in a triangle. 

Step 1:
Split each diagram into triangles in such a way that you are only splitting the angles at each vertex. 

Step 2: 
Use your understanding of the sum of the interior angles of a triangle to find the total interior angle of the shape in question.

Step 3:
Compare all the values of every shape and figure out a general rule for a polynomial of any number of sides. 

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Question 1

1.

Use a single line to break the quadrilateral into 2 triangles.

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Question 2

2.

Hence calculate the sum of the total interior angles of a quadrilateral.

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Question 3

3.

Use two lines to break the pentagon into 3 triangles.

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Question 4

4.

Hence calculate the sum of the total interior angles of a pentagon.

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Question 5

5.

Use three lines to break the hexagon into 4 triangles.

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Question 6

6.

Hence calculate the sum of the total interior angles of a hexagon.

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Question 7

7.

Use four lines to break the heptagon into 5 triangles.

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Question 8

8.

Hence calculate the sum of the total interior angles of a heptagon.

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Question 9

9.

Use five lines to break the octagon into 6 triangles.

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Question 10

10.

Hence calculate the sum of the total interior angles of an octagon.

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Question 11

11.

Use six lines to break the nonagon into 7 triangles.

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Question 12

12.

Hence calculate the sum of the total interior angles of a nonagon.

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Question 13

13.

Use seven lines to break the decagon into 8 triangles.

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Question 14

14.

Hence calculate the sum of the total interior angles of a decagon.

Question 15

15.

Complete the table below using the information you gathered so far.