> > 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?

## 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?

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