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Yes, there is a maximum number. Recall that the sum of the exterior angles is 360 degrees regardless of what kind of polygon it is.

Since an obtuse angle is and angle that is greater than 90 degrees, four of them would be greater than 360 degrees so we could not have that in a polygon.

Therefore, the maximum number of obtuse angles is 3.

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Q: Is there a maximum number of obtuse exterior angles a polygon can have?
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