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One maximum. An obtuse angle is greater than 90 degrees. Since a triangle must have all 3 angles add up to exactly 180 degrees, if there is an angle greater than 90 degrees, the other two must be less than 90 degrees together (whatever 180-B is, where B is the obtuse angle), meaning neither angle could be greater than 45 degrees, and thus the other two will always be acute.

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Q: How many obtuse angles can a triangle have?
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