Use this applet to investigate the sum of angles in polygons. Is there a pattern? Can you predict the sum of the angles in a 20-sided polygon?

Use the applet...

Duane Habecker, Created with GeoGebra

Directions:

- Create a triangle of your choice. Measure each angle of the triangle and find their sum. Try one or two more triangles. Is their angle sum always the same? Record the angle sum for triangles in the table below. and quadrilaterals in the table below.
- Create a quadrilateral of your choice. Measure each angle of the quadrilateral and find their sum. Try one or two more quadrilaterals. Is their angle sum always the same? Record the angle sum for quadrilaterals in the table below.
- Continue to fill in the table for pentagons and hexagons. Find a pattern.
- What is the relationship between the number of sides on the shape and the sum of the angles?

Polygon | Number of sides |
Sum of angles |

Triangle | ||

Quadrilateral |
||

Pentagon |
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Hexagon |
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Septagon | ||

Octagon |

Extension: What is the sum of the angles in a 20-sided figure?