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ABCDEF is a concave hexagon with exactly one interior angle greater than 180 degrees. (The diagram below is not drawn to scale.) Noah measured the marked angles, getting 80,85,95,105,120,125. What interior angle measure of the hexagon, in degrees, is missing from Noah's list?

 

 Jan 17, 2021

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Let's say the missing angle is x. Then the corresponding angle is 360-x. So when we replace x with 360-x, the sum changes by 360-2x. The current sum is 610 but we want it to be 720. That means 360-2x is 120 so x is 120.

:D

 Jan 17, 2021

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