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: [br][list][*]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?[br][/*][/list]

Quadrilateral

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

Pentagon

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

Hexagon

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

Heptagon

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

Octagon

Based on your observations,answer the following: [br]How many sides does the polygon have? [br]How many triangles are formed on draging the slider from left to right?[br]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. [br][br]The sum of the measures of the N interior angles of an N-gon is: _________________________.