Solution:
Given:
The three interior angles of a triangle are;
[tex]6x+1,9x+4,6x-14[/tex]
To find the value of x, we use the theorem for the sum of interior angles in a triangle.
The sum of interior angles in a triangle is 180 degrees.
Hence,
[tex]\begin{gathered} (6x+1)+(9x+4)+(6x-14)=180^0 \\ \text{Collecting the like terms,} \\ 6x+9x+6x+1+4-14=180 \\ 21x-9=180 \\ 21x=180+9 \\ 21x=189 \\ \text{Dividing both sides by 21 to get the value of x,} \\ x=\frac{189}{21} \\ x=9 \end{gathered}[/tex]
Therefore, the value of x is 9.
