Question 680296

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+(x-1)+2x=180}}}

 {{{ x+x-1+2x=180}}}

{{{ 4x=180+1}}}

{{{ 4x=181}}}

{{{ x=181/4}}}

{{{ 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