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

Question 127556: Prove the following statement: If a triangle has one obtuse angle, then the other two angles are acute.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

Use indirect reasoning to explain why a triangle cannot have more than one obtuse angle.
First, assume that a triangle does have

.
The measure of an obtuse angle is greater than degrees. Hence, the sum of the measures of angles is than degrees, and the sum of the measures of angles is greater that degrees.
The sum of the angles of a triangle, however, degrees.
Therefore,

in a triangle can be .

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