We have here two parallel lines, m, and n, cut by a transversal (t). In this case, we have that the corresponding angles are congruent.
We have that both equations represent corresponding angles. Then, we have that:
[tex](7x-4)=(5x+10)[/tex]
Now, we need to solve these equations for x. We can proceed as follows:
1. Subtract 5x from both sides of the equation:
[tex]7x-5x-4=5x-5x+10\Rightarrow2x-4=0+10\Rightarrow2x-4=10[/tex]
2. Add 4 to both sides of the equation:
[tex]2x-4+4=10+4\Rightarrow2x+0=14\Rightarrow2x=14[/tex]
3. And finally, divide both sides of the equation by 2:
[tex]\frac{2x}{2}=\frac{14}{2}\Rightarrow x=7[/tex]
Therefore, the value for x is x = 7.
