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Polygon Angle Sums: Quadrilateral through Octagon

Your objective: Find a rule for the sum of the interior angles of a polygon.

For each polygon, drag the slider from left to right. As you drag the slider, make note of the following:
  • What is happening to the angles?
  • Are there any other shapes being formed within the polygon?
  • How might this help you figure out the sum of the interior angles?

Quadrilateral

Based on your observations,answer the following: How many sides does the polygon have? How many triangles are formed on draging the slider from left to right? What is the sum of interior angles of a quadrilateral?

Pentagon

Based on your observations,answer the following: How many sides does the polygon have? How many triangles are formed on draging the slider from left to right? What is the sum of interior angles of a pentagon?

Hexagon

Based on your observations,answer the following: How many sides does the polygon have? How many triangles are formed on draging the slider from left to right? What is the sum of interior angles of a hexagon?

Heptagon

Based on your observations,answer the following: How many sides does the polygon have? How many triangles are formed on draging the slider from left to right? What is the sum of interior angles of a heptagon?

Octagon

Based on your observations,answer the following: How many sides does the polygon have? How many triangles are formed on draging the slider from left to right? What is the sum of interior angles of an octagon?

Conclusion:

Use your answers to the previous questions to find a general formula for the sum of the measures of the interior angles of a polygon in terms of the number of sides, N. The sum of the measures of the N interior angles of an N-gon is: _________________________.