Tell wether the statement is always, so
Etimes, or never true. Justify your reasoning and i clude example .The sum of any two angle measures in an acute triangle is greater than 90 degree.
since no angle is greater than 90 degrees, if the angles are A,B,C, then since C<90, and A+B+C = 180
A+B > 90
always true.
To determine whether the statement "The sum of any two angle measures in an acute triangle is greater than 90 degrees" is always, sometimes, or never true, we need to analyze the properties of acute triangles.
First, let's define an acute triangle. An acute triangle is a triangle where all three angles are less than 90 degrees.
Now, let's consider why the statement might be true in some cases. In an acute triangle, each angle measures less than 90 degrees. If we take any two angles, their sum will be less than 180 degrees (the sum of all three angles in any triangle). Therefore, the sum of any two angle measures in an acute triangle will always be less than 180 degrees.
Since we know that any two angles in an acute triangle will be less than 180 degrees, we can conclude that the sum of any two angle measures in an acute triangle will always be greater than 90 degrees. Therefore, the statement is always true.
Example: Let's consider an acute triangle with angle measures of 40 degrees, 50 degrees, and 80 degrees. If we choose any two angles, such as 40 degrees and 50 degrees, their sum is equal to 90 degrees, which is greater than 90 degrees.
In conclusion, any two angle measures in an acute triangle will always have a sum greater than 90 degrees.