Verify that the measure of a vertex angle in a regular polygon is (n − 2)180°/n (Theorem 2.3), by completing the given table as follows: (i) Sketch regular polygons with four, five, six, and more sides, and (ii) divide each polygon into triangles by drawing all possible diagonals from one vertex. Use inductive reasoning to develop the formula given in Theorem 2.3.
Number of Sides and Angles in a Polygon | Number of Triangles into Which the Polygon Can Be Divided | Sum of Angle Measures in the Polygon | Measure of One Angle in the Polygon |
3 | 1 | 180°
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4 | 2 | 2(180°) = 360° |
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5 |
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6 |
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8 |
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10 |
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n |
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