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Interior Angles in Polygons Exploration

Author:Bradford L Dalton, Tim Brzezinski, Alfonso Garcia, Mdm Lim

INSTRUCTIONS

Your objective: Find a rule for the sum of the interior angles of a polygon (for today). 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. 2) For each polygon, drag the slider from left to right. As you drag the slider, answer the questions along the way. Have fun!

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?

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  • A
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  • D
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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 also change the shape of the triangle by moving vertices and creating different triangles.

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  • D
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Quadrilateral

Sum of the 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. Also try changing the shape of the quadrilateral by moving the vertices.

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Interior Angles in a Quadrilateral - Making connections

Using our previous answer and the fact that the sum of the interior angles in a triangle = 180o we can now determine the sum of the interior angles of a quadrilateral. Which would be the correct calculation?

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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. Also try changing the shape of the quadrilateral by moving the vertices.

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Pentagon

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

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  • B
  • C
  • D
Check my answer (3)

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.

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Interior Angles in a Hexagon - Making connections

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

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  • A
  • B
  • C
  • D
Check my answer (3)

Summarize

Write a summary of how to find the interior angles of a polygon- Include a formula for extra credit

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