One exterior angle of a regular polygon measures 30. What is the sum of the polygon's interior angle measures?

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Dec 22, 2015

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Exterior angle of #n# sided regular polygon is found by the formula

#360/n#

We are given one exterior angle is #30^o#

#360/n = 30#

#=>n = 360/30#

#=> n=12#

The polygon is a dodecagon.

The sum of the interior angles is found by the formula

#(n-2)*180^o#

Here we found the number of sides is 12, therefore #n=12#

#(12-2)*180^o#

#=10*180^o#

#=1800^o# Answer

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