# Interior and Exterior Angles in Polygons Exploration

- Author:
- Alfonso Garcia, Tim Brzezinski

- Topic:
- Angles, Geometry, Mathematics, Polygons

## INSTRUCTIONS

## Triangle

## Interior angles in a Triangle

Move the slider "Show Interior Angles" slowly and watch what happens. What is the best description of the angle that is created by the sum of these angles?

## Interior angles in a Triangle

Move the slider "Show Interior Angles" slowly and watch what happens. What is the sum of the interior angles in any triangle? You can change the shape of the triangle by moving vertices.

## Interior Angles - Explanation

Justify your answer to the above question, how do you know from the applet?

## Exterior Angles in a Triangle

Now play with the slider "Show Exterior Angles" and notice what happens when you slide it all the way to the right side. What is the best description for the sum of the exterior angles?

## Quadrilateral

## Interior Angles in a Quadrilateral

Move the slider "Show Interior Angles" slowly and watch what happens once it gets to the right side. How many triangles are created inside the quadrilateral? Write your answer as a number. You can change the shape of the quadrilateral by moving the vertices.

## Interior Angles in a Quadrilateral - Making connections

Using our previous answer and the fact that the sum of the interior angles in a triangle = 180^{o
}we can determine the sum of the interior angles of a quadrilateral.
Which is the correct calculation?

## Exterior angles in a Quadrilateral

Now move the slider "Show Exterior Angles" slowly to the right and notice what happens when it gets to the end. What is the sum of the exterior angles of a quadrilateral?

## Pentagon

## Interior Angles in a Pentagon

Move the slider "Show Interior Angles" slowly and watch what happens once it gets to the right side. How many triangles are created inside the pentagon? Write your answer as a number. You can change the shape of the quadrilateral by moving the vertices.

## Pentagon

Using our previous answer and the fact that the sum of the interior angles in a triangle = 180^{o
}we can determine the sum of the interior angles of a pentagon.
Which is the correct calculation?

## Exterior angles in a Pentagon

Now move the slider "Show Exterior Angles" slowly to the right and notice what happens when it gets to the end. What shape is made by the sum of the exterior angles and how many degrees does it equal?

## Hexagon

## Hexagon

Move the slider "Show Interior Angles" slowly and watch what happens once it gets to the right side. How many triangles are created inside the hexagon? Write your answer as a number.

## Interior Angles in a Hexagon - Making connections

Using our previous answer and the fact that the sum of the interior angles in a triangle = 180^{o
}we can determine the sum of the interior angles of a hexagon.
Which is the correct calculation?

## Exterior angles in a Hexagon

Now move the slider "Show Exterior Angles" slowly to the right and notice what happens when it gets to the end. What is the sum of the exterior angles?

## Reflecting

Give me two ideas of what you discovered in this activity.

## The Heptagon - sum of interior angles.

A heptagon is a polygon with 7 sides.
Based on what you have experienced here, see if you can come up with a way to find out the ** sum of the interior angles **for this shape.

## The Heptagon - sum of exterior angles.

What would be the** sum of the exterior angles** of a heptagon?