Calculate Single Missing Angle of Polygon

devitius

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See attached image for question.

I know this should be easy, but the answer just doesn't click for me?
 

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\(\displaystyle One \ way:\)

\(\displaystyle We \ have \ three \ triangles \ enclosed \ in \ the \ polygon;\)

\(\displaystyle hence, \ (3)(180^0)-480^0 \ = \ 60^0\)
 
Thanks.

Interior angle of a polygon = (n - 2) x 180° or (n - 2) x ? radians , where n = number of sides

This particular question was actually directed toward year 9 students in what was a generic numeracy test, which makes me wonder whether they'd be expected to know specically about this formula for the interior angle of a polygon or whether they could roughly estimate the angle in some other fashion.
 
\(\displaystyle On \ this \ one, \ I \ guess \ that \ it \ depends \ on \ the \ perspicacity \ of \ the \ student.\)
 
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