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Question Find the measure of a single exterior angle of a regular decagon. If necessary, round to the nearest tenth. Answer Attempti out of 2

Ask by Turnbull Williams. in the United States
Mar 11,2025

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Answer

Each exterior angle of a regular decagon is \(36.0^\circ\).

Solution

1. For any polygon, the sum of the exterior angles is given by \(360^\circ\). 2. A decagon has 10 sides, so a regular decagon has 10 congruent exterior angles. 3. The measure of a single exterior angle is: \[ \frac{360^\circ}{10} = 36^\circ \] 4. No rounding is necessary, so the measure of a single exterior angle is \(36.0^\circ\).

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Bonus Knowledge

To find the measure of a single exterior angle of a regular decagon, you can use the formula for the exterior angle of a regular polygon, which is \( \frac{360}{n} \), where \( n \) is the number of sides. For a decagon, where \( n = 10 \), the calculation goes like this: \( \frac{360}{10} = 36 \) degrees. So, each exterior angle measures 36 degrees! Now, if you were to mistakenly calculate the interior angle instead of the exterior angle—watch out! The interior angle of a regular decagon can be calculated using \( (n-2) \times 180/n \), resulting in 144 degrees. But remember, once you have the interior angle, just subtract it from 180 to find the exterior angle, reminding you to always double-check which angle you need!

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