SOLUTION: can an acute triangle have the measurements of x, x-1 and 2x and still be a triangle

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Question 680296: can an acute triangle have the measurements of x, x-1 and 2x and still be a triangle
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

If you are given the measurements of angles, than you have to follow these definitions.

An acute triangle is a triangle where all three internal angles are acute (less than 90 degrees).
In any triangle, two of the interior angles are always acute (less than 90 degrees)*, so there are three possibilities for the third angle:
Less than 90° - all three angles are acute and so the triangle is acute.
Exactly+90° - it is a right triangle
Greater than 90° (obtuse): the triangle is an obtuse triangle

if the measurements of angles are:+x, x-1 and 2x, than

+x%2B%28x-1%29%2B2x=180
+x%2Bx-1%2B2x=180
+4x=180%2B1
+4x=181
+x=181%2F4
+x=45.25
so, x-1=44.25 and 2x=90.5
since 2x=90.5 or greater than 90°, a triangle cannot be acute, the triangle is an obtuse triangle