Using an $11$ sided polygon the most acute angles you could have is $4$ with $7$ obtuse angles. You can find this out by taking $1620$ which is the total number of degrees all of the sides should add up to be. If you take obtuse angles as $180$ degrees and $90$ degrees for acute angles to make it easier, then you can plug in sides to find what would add up to be $1620.$ There are $11$ sides so if you take $6$ obtuse angles and $5$ acute angles it adds up to be $1540$ which is too small. If you take $7$ obtuse angles and $4$ acute angles it adds up to be $1620.$

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