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### GSP Investigation: Sum of Angles in a Polygon

posted Mar 19, 2014, 4:03 PM by Michael Dreyfus-Pai   [ updated Mar 20, 2014, 12:00 PM ]
You may already know what the sum of the angle measures is in any triangle. In this activity, you'll see how that sum is related to the sum of the angle measures in other polygons.

## Step 1: Construct and Measure a Triangle's Angles (Group Work)

1. Construct triangle ABC
2. Measure each interior angle in ABC
3. Calculate the sum of the angles in ABC
4. Move one or more points in ABC and observe how the measures and sum changes.

## Step 2: Construct and Measure Polygon Angles (Individual)

1. Construct quadrilateral EFDG, pentagon HIJKL, and hexagon MNOPQR
2. Measure each angle in EFDG.
3. Calculate the sum of angles in EFDG. Place the sum under the figure and record it on your table.
4. Choose a vertex of EFDG and draw all diagonals from that point. No two diagonals should intersect.
5. Record the number of triangles formed in the table.
6. Repeat steps 2 - 3 for each additional polygon listed in the table. Once you see a pattern, you can stop constructing/measuring and fill in the table based on that pattern.

## Tables (found on worksheet)

 Sides Polygon Sum of Interior Angles Triangles 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Septagon 8 Octogon 10 Decagon

Question 1: Write a rule you can use to get from the number of triangles in a polygon to the sum of its interior angles.  Test your rule using the table below:

 Triangles t 1 2 3 4 5 6 10 Rule

Question 2: What is the relationship between number of triangles (t) and number of sides (n)?  _____________________________

Question 3: Now write a rule to get from sides to sum of interior angles and test it:

 Sides n 3 4 5 6 8 10 15 Rule
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Michael Dreyfus-Pai,
Mar 19, 2014, 4:47 PM