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By definition, the compliment to an angle is an angle whose measure would combine with the first to reach 90 degrees. Also, by definition, an obtuse angle is an angle whose measure is greater than 90 degrees. There is no angle that can be added to an angle larger than 90 degrees that will cause that angle to be 90 degrees (because the measure of an angle is inherently positive.) Therefore, there is no compliment to an obtuse angle.

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Q: Is there an angle that is the complement of an obtuse angle?
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