Interior Angles of a Polygon - tandrageemaths
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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