D.G. 5.1: Polygon Angle Sums: Quadrilateral through Octagon

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

[b]Answer all questions on binder paper.[/b][br][br][br]1) Before you begin, make sure the box labeled "Show Interior Angles" is the only one checked. You will be working on that part only for today.[br][br]2) 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, what is the sum of the measures of the interior angles of a quadrilateral?

Pentagon

Based on your observations, what is the sum of the measures of the interior angles of a pentagon?

Hexagon

Based on your observations, what is the sum of the measures of the interior angles of a hexagon?

Heptagon

Based on your observations, what is the sum of the measures of the interior angles of a heptagon?

Octagon

Based on your observations, what is the sum of the measures of the interior angles of a 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. (Note: if a polygon has N sides, it is called an N-gon.)[br][br]The sum of the measures of the N interior angles of an N-gon is: _________________________.