Pregunta
Find the measure of a single exterior angle of a regular 11-gon. If necessary, round to the nearest tenth.
Ask by Zimmerman Greene. in the United States
Mar 11,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
Each exterior angle of a regular 11-gon is approximately 32.7 degrees.
Solución
1. The formula for the measure of an exterior angle of a regular \( n \)-gon is
\[
\text{Exterior Angle} = \frac{360^\circ}{n}.
\]
2. For a regular 11-gon, substitute \( n = 11 \) into the formula:
\[
\text{Exterior Angle} = \frac{360^\circ}{11} \approx 32.7273^\circ.
\]
3. Rounding to the nearest tenth gives:
\[
32.7^\circ.
\]
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To find the measure of a single exterior angle of a regular 11-gon, 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 an 11-gon, this becomes \( \frac{360°}{11} \approx 32.727°. \) Rounding to the nearest tenth, the measure of a single exterior angle is approximately **32.7°**. Now, just envision packing a pizza with 11 identical slices—each slice represents one exterior angle! As you chow down, you can mentally keep track of how each exterior angle adds up to a full circle, reminding you that those 11 slices take a total of 360°, with each slice being about 32.7° of deliciousness!
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