Answer:
Angle [tex]A=116\°[/tex]
Step-by-step explanation:
Given:
Three angles of a triangle ABC.
[tex]A(9x+17)\\B(3x-4)\\C(6x-31)[/tex]
Angle sum of a triangle is always = 180°
∴ [tex]A+B+C=180\°[/tex]
Plugging in values of [tex]A,B \ and\ C[/tex]
[tex](9x+17)+(3x-4)+(6x-31)=180[/tex]
Combining like terms.
[tex]9x+3x+6x+17-4-31=180[/tex]
[tex]18x-18=180[/tex]
Adding 18 both sides.
[tex]18x-18+18=180+18[/tex]
[tex]18x=198[/tex]
Dividing both sides by 18.
[tex]\frac{18x}{18}=\frac{198}{18}[/tex]
∴ [tex]x=11[/tex]
Angle [tex]A=9x+17[/tex]
Plugging in value of [tex]x[/tex]
Angle [tex]A=9(11)+17[/tex]
Angle [tex]A=99+17[/tex]
Angle [tex]A=116\°[/tex]
