Interior and Exterior Angles in Polygons Exploration

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?

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.

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

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?

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.

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?

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?

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.

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?

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?

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.

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?

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?

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

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.

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