Answer:
The greatest angle is [tex]18x-7[/tex]
Explanation:
According to angle sum property of a triangle, sum of all the angles of a triangle is equal to [tex]180[/tex]°.
The given angles of a triangle are [tex]18x-7,12x+9,4x[/tex]
Therefore,
[tex]18x-7+12x+9+4x=180[/tex]°
[tex]34x+2=180[/tex]°
[tex]34x=178[/tex]°
[tex]x=\frac{178}{34}=\frac{89}{17}[/tex]
[tex]18x-7=18(\frac{89}{17})-7=\frac{1602-119}{17}=\frac{1483}{17}[/tex]≈ 87.2°
[tex]12x+9=12(\frac{89}{17})+9=\frac{1068+153}{17}=\frac{1221}{17}[/tex] ≈ 71.8°
[tex]4x=4(\frac{89}{17})=\frac{356}{17}[/tex] ≈ 20.9°
Therefore, greatest angle is [tex]18x-7[/tex]
