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What is the measure of each angle of a regular 13-gon? If necessary, round to the nearest tenth.

Ask by Washington Salinas. in the United States
Mar 11,2025

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Answer

Each interior angle of a regular 13-gon is approximately \( 152.3^\circ \).

Solution

1. A regular \( n \)-gon has interior angles given by the formula: \[ \text{Interior Angle} = \frac{(n-2) \times 180^\circ}{n} \] 2. For a 13-gon, substitute \( n = 13 \): \[ \text{Interior Angle} = \frac{(13-2) \times 180^\circ}{13} = \frac{11 \times 180^\circ}{13} \] 3. Compute the product in the numerator: \[ 11 \times 180^\circ = 1980^\circ \] 4. Now, divide by 13: \[ \text{Interior Angle} = \frac{1980^\circ}{13} \approx 152.3^\circ \] 5. Therefore, each interior angle of a regular 13-gon is approximately \( 152.3^\circ \).

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Bonus Knowledge

To find the measure of each interior angle of a regular 13-gon, you can use the formula for the interior angle of a regular polygon: \[\text{Interior angle} = \frac{(n - 2) \times 180^\circ}{n},\] where \(n\) is the number of sides. For a 13-gon: \[\text{Interior angle} = \frac{(13 - 2) \times 180^\circ}{13} = \frac{11 \times 180^\circ}{13} \approx 153.8^\circ.\] So, each angle measures approximately 153.8 degrees when rounded to the nearest tenth. To put this in a fun context, imagine hosting a cool polygon party. Your 13-gon friends are all standing in a perfect circle, and each of their angles is just enough so they don't bump into each other while showing off their sharp geometric styles. So, keep that angle in mind while you throw your next angle-themed get-together!

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