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If the measure of one exterior angle of a regular polygon is 30 degrees how many sides does the polygon have?

If the measure of one exterior angle of a regular polygon is 30 deg...

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If the measure of one exterior angle of a regular polygon is 30 degrees how many sides does the polygon have?

If the measure of one exterior angle of a regular polygon is 30 degrees how many sides does the polygon have?

Answer

[tex]From\ formula\ for\ interior\ angle\ in
egular\ \\\\ \alpha = \pi -\frac{2 \pi }{n}\ \\\
-number\ of\ sides\\\\ \alpha =180-30=150 degress\\\\ \alpha = \pi - \frac{2 \pi }{n} |- \pi \\\\ \alpha - \pi= -\frac{2 \pi }{n}|*n\\\\ (\alpha - \pi )n=-2 \pi \\\
= \frac{-2 \pi }{ \alpha - \pi } \\\
= \frac{-360}{150-180} \\\
=\frac{-360}{-30}=12 \\\\This\ polygon\ has\ 12\ sides.
[/tex]

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Virtual Teaching Assistant: John B.
Question Level: Basic
Karma: Free
Upload Date: 5/31/2017

This 42 words question was answered by John B. on StudySoup on 5/31/2017. The question contains content related to Math Since its upload, it has received 353 views.

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