SOLUTION: Prove the following statement: If a triangle has one obtuse angle, then the other two angles are acute.

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Question 127556: Prove the following statement: If a triangle has one obtuse angle, then the other two angles are acute.
Answer by MathLover1(20849) About Me  (Show Source):
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Use indirect reasoning to explain why a triangle cannot have more than one obtuse angle.
First, assume that a triangle does have more+than+one+obtuse+angle.
The measure of an obtuse angle is greater than 90 degrees. Hence, the sum of the measures of two+obtuse+angles is greater than 180 degrees, and the sum of the measures of three+obtuse angles is greater that 270 degrees.
The sum of the angles of a triangle, however, equals+180+degrees.
Therefore, only+one+angle in a triangle can be obtuse.