Polygon Angle Sum: 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 can these other shapes being formed inside the polygon help you figure out the sum of the interior angles?[br][/*][/list]
Quadrilateral
Based on your observations,answer the following:
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? (Hint: Use angle sum property of a triangle)
Pentagon
Based on your observations,answer the following:
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? (Hint: Use angle sum property of a triangle)
Hexagon
Based on your observations,answer the following:
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? (Hint: Use angle sum property of a triangle)
Heptagon
Based on your observations,answer the following:
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? (Hint: Use angle sum property of a triangle)
Octagon
Based on your observations,answer the following:
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 octagon? (Hint: Use angle sum property of a triangle)
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: _________________________.