Sums of Polygon Angles

Melissa McGarity

Objectives: Students will explore and discover patterns in the angle sums of n-gons. Students will learn the formula for the angle sum of an n-gon.

Materials: Student worksheet and GSP access

Sums of Polygon Angles

NAME:____________________

Instructions: Use GSP to do the exploration below.

1. Open a new GSP sketch.

2. Across the top of your sketch, draw a triangle, quadrialteral, and pentagon. In the middle of your sketch, construct a hexagon, septagon, and octagon.

3. Measure the three angles of the triangle and arrange the measurements under the triangle.

4. Measure the four angles of the quadrilateral and arrange the measurements under the triangle.

5. Repeat finding the angle measurements and arranging them under the corresponding polygon for each polygon you have created.

6. Calculate the sum of the angle measurements for each polygon and put it inside of the corresponding polygon.

7. Drag the vertices of each polygon and observe the angle measures and the sum of the angles.

What happens to the angle measurements when you drag the vertices?

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What happens to the sum of the angle measurements when you drag the vertices?

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8. Complete the table below.

 Polygon Number of Sides Sum of Angles Triangle Quadrilateral Pentagon Hexagon Septagon Octagon

Describe the pattern in the "Sum of Angles" column.

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Describe the pattern in the sum of angles as you increased the number of sides in the polygon.

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What would the sum of angles be for a polygon with 9 sides?

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What would the sum of angles be for a polygon with 10 sides?

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What would the sum of angles be for a polygon with n sides? (Feel free to discuss with other people and groups).

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9. Get ready for class discussion.