Question 67783: Prove the following statement:
If a triangle has one obtuse angle, then the other two angles are acute.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Prove the following statement:
If a triangle has one obtuse angle, then the other two angles are acute.
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The sum of the angles of a triangle = 180 degrees by definition or assumption.
Let A be an obtuse angle in the triangle.
The measure of A is (90 + x) degrees where x is positive, by definition of obtuse.
The sum of the remaining two angles 180-A since the sum is 180.
Then 180-(90+x)=90-x and x is positive by substitution.
Therefore the sum of the remaining two angles is less than 90 by arithmetic.
Therefore both of the other two angles is acute. QED
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Cheers,
Stan H.
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