how many sides does a regular polygon have if each exterior angle measures 30

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Guest Mar 9, 2015

+5

Best Answer

The exterior angles of any regular or non-concave sided shape is 360 degrees

so, $${\frac{{\mathtt{360}}}{{\mathtt{30}}}} = {\mathtt{12}}$$ which is the answer.

Guest Mar 9, 2015

Guest · Answer 1 · 2015-03-09T10:05:29

The exterior angles of any regular or non-concave sided shape is 360 degrees

so, $${\frac{{\mathtt{360}}}{{\mathtt{30}}}} = {\mathtt{12}}$$ which is the answer.

CPhill · Answer 2 · 2015-03-09T09:45:09

If the exterior angle is 30, the interior angle is supplementary to this = 150

And we have

(n - 2)(180) / n = 150

(n - 2)(180) = 150n

180n - 360 = 150n rearrange

30n = 360 divide by 30 on both sides

n = 12 sides {a dodecagon}