SOLUTION: Four interior angles of a hexagon are 130, 160, 112 and 80. If the reamaining angles are equal, find the size of each of them.

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Question 1010403: Four interior angles of a hexagon are 130, 160, 112 and 80. If the reamaining angles are equal, find the size of each of them.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the interior angles of a polygon with n sides/angles is
%28n-2%29180%5Eo ,
so the sum of the 6 interior angles of a hexagon is
%286-2%29%2A180%5Eo=4%2A180%5Eo=720%5Eo .
The four given angles add up to
130%5Eo%2B160%5Eo%2B112%5Eo%2B80%5Eo=482%5Eo ,
so the sum of the remaining 6-2=4 angles is
720%5Eo-482%5Eo=238%5Eo .
That means that each of the remaining "equal" angles measures
238%5Eo%2F2=highlight%28119%5Eo%29 .