The sum of the interior triangles in a triangle is 180, so if we add all the angle measures together, we should get 180. Therefore, we can make an equation like this,
[tex]110-2x+x+50+5x-40=180[/tex]
Simplify this.
[tex]4x+120=180[/tex]
[tex]4x=60[/tex]
[tex]x=15[/tex]
Now we can find each angle measure.
[tex]110-2x[/tex]
[tex]110-2(15)[/tex]
[tex]110-30[/tex]
[tex]80[/tex]
[tex]x+50[/tex]
[tex]15+50[/tex]
[tex]65[/tex]
[tex]5x-40[/tex]
[tex]5(15)-40[/tex]
[tex]75-40[/tex]
[tex]35[/tex]
So the angle labeled [tex]110-2x[/tex] is the largest angle in the triangle.
