We are given that the lines m and n are parallel and the line t is a transversal line.
The angles given in the figure must add up to 180° as per the straight-line angle property.
So, we can set up the following equation
[tex](x+14)\degree+(4x-9)\degree=180\degree[/tex]
Let us solve the equation for x.
[tex]\begin{gathered} (x+14)+(4x-9)=180 \\ x+4x+14-9=180 \\ 5x+5=180 \\ 5x=180-5 \\ 5x=175 \\ x=\frac{175}{5} \\ x=35 \end{gathered}[/tex]
Therefore, the value of x is 35
