7.1 Investigate Polygon Interior Angle Sum

Question:

What is the sum of the measures of the Interior Angles of a Convex n-gon?

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1. In each polygon below, [i]draw all of the diagonals[/i] from 1 vertex. Notice that the diagonals divide the polygon into triangles. (Click on the 1st triangle then select the Segment button above in order to draw).[br][br]2. By the [b]Triangle Angle Sum Theorem[/b], the sum of the interior angles of a triangle is [math]180^o[/math]. Use this theorem to complete the table.

7.1 Investigating Polygon Interior Angle Sum

Based on the data in your table, which of the following expressions would you use to determine the number of triangles in an [i]n-gon[/i]?

[math]n+2[/math] [math]n-2[/math] [math]n-1[/math] [math]n+1[/math]

Based on the data in your table, which of the following expressions would you use to determine the SUM of the measures of the interior angles of an [i]n-gon[/i]?

[math]180\cdot\left(n-3\right)[/math] [math]180\cdot\left(n-2\right)[/math] [math]180\cdot\left(n+3\right)[/math] [math]180\cdot\left(n+2\right)[/math]

7.1 Investigate Polygon Interior Angle Sum

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7.1 Investigating Polygon Interior Angle Sum

Information: 7.1 Investigate Polygon Interior Angle Sum