Google Classroom
GeoGebraGeoGebra Classroom

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:
  • 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?

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? (Hint: Use angle sum property of a triangle)

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? (Hint: Use angle sum property of a triangle)

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? (Hint: Use angle sum property of a triangle)

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? (Hint: Use angle sum property of a triangle)

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 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. The sum of the measures of the N interior angles of an N-gon is: _________________________.