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

- Author:
- Julian Ornelas, Tim Brzezinski

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

**Answer all questions on binder paper.**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. 2) 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, 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.)
The sum of the measures of the N interior angles of an N-gon is: _________________________.