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ind the interior angle and exterior angle of each regular polygon. Round to the nearest tenth if necessary. \( \begin{array}{l}\text { 11. Heptagon } \\ \text { 13-gon } \\ \qquad \begin{array}{l}\text { Interior } \angle= \\ \text { Exterior } \angle=\end{array} \\ \text { Interior } \angle= \\ \text { Exterior } \angle=\square\end{array} \)

Ask by Deleon Johnson. in the United States
Feb 27,2025

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Heptagon: - Interior angle ≈ 128.6° - Exterior angle ≈ 51.4° 13-gon: - Interior angle ≈ 152.3° - Exterior angle ≈ 27.7°

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Bonus Knowledge

To find the interior and exterior angles of a regular polygon, you can use specific formulas. For an n-sided polygon, the interior angle can be calculated as \( \frac{(n - 2) \times 180}{n} \), and the exterior angle is given by \( \frac{360}{n} \). For a heptagon (7 sides): - **Interior angle**: \( \frac{(7 - 2) \times 180}{7} = \frac{5 \times 180}{7} \approx 128.6° \) (rounded to the nearest tenth) - **Exterior angle**: \( \frac{360}{7} \approx 51.4° \) (rounded to the nearest tenth) For a 13-gon (13 sides): - **Interior angle**: \( \frac{(13 - 2) \times 180}{13} = \frac{11 \times 180}{13} \approx 150.0° \) (rounded to the nearest tenth) - **Exterior angle**: \( \frac{360}{13} \approx 27.7° \) (rounded to the nearest tenth) So, for each polygon: **Heptagon** Interior angle = 128.6° Exterior angle = 51.4° **13-gon** Interior angle = 150.0° Exterior angle = 27.7°

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