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

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Question 238515: Prove the following statement:
If a triangle has one obtuse angle, then the other two angles are acute.
Found 2 solutions by Fombitz, nyc_function:
Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
For every triangle,
A%2BB%2BC=180
where A,B,C are the angles.
An obtuse angle is an angle greater than 90 degrees.
Let A be an obtuse angle.
Then A=90+e, where e is a positive value, less than 90.
90%2Be%2BB%2BC=180
e%2BB%2BC=90
B and C cannot equal 0.
0%3Ce%3C90
Then
B%2BC%3C90
0%3CB%3C90
0%3CC%3C90
which means they are both acute.

Answer by nyc_function(2645) About Me  (Show Source):
You can put this solution on YOUR website!
An obtuse angle is an angle whose measure is more than 90 degress but less than 180 degrees.
The sum of the measures of the angles of a triangle is 180 degrees.
Given a triangle having one obtuse angle, it follows that the other two angles must be acute or less than 90 degrees because the sum of the angles of a triangle = 180 degrees.