Interior Angles of a Polygon



Interior Angles of a Polygon

You can calculate the interior angles of a polygon by splitting the polygon into Triangles. You will form a series of triangles. The angle sum of each triangle is 180˚. In the example below the quadrilateral has been split into 2 triangles. Two triangles with angles of 180˚ form a quadrilateral with a 360˚ angle (2 x 180˚ = 360˚)

1. Copy the table below into your exercise books. Complete the table and underneath complete a diagram for each polygon type that you know.

|Polygon |No of sides |No of triangles |Sum of all angles |

|Triangle |3 |1 |1 x 180 = 180 |

|Quadrilateral |4 |2 |2 x 180 = 360 |

|Pentagon | | | |

|Hexagon | | | |

|Heptagon | | | |

|Octagon | | | |

|Nonagon | | | |

|Decagon | | | |

2. There is a formula that links the number of sides that a polygon has (N) with the total sum of the interior angles for a polygon. Can you work out what that formula is?

3. Use the formula you have found to calculate the angle sum for the following polygons:

a) 11 sides b) 14 sides c) 19 sides d) 21 sides

e) 24 sides f) 43 sides g) 65 sides h) 77 sides

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