Answer:
![x=12](https://img.qammunity.org/2021/formulas/mathematics/middle-school/kzh72we7ptn8hlgavxhsl5e208kjtiramm.png)
Explanation:
First, note that the angles shown are vertical angles. In other words, the two equations are equivalent to each other.
Therefore, set the equations equal to each other and solve for x;
![6x+7=8x-17](https://img.qammunity.org/2021/formulas/mathematics/college/m0r1b8jklurzko9dlb5fyr9t7nwpms78o3.png)
Add 17 to both sides:
![6x+24=8x](https://img.qammunity.org/2021/formulas/mathematics/college/e57xskfn9vihgtuxlyb4jdmyjpzh4uyg9h.png)
Subtract 6x from both sides:
![24=2x](https://img.qammunity.org/2021/formulas/mathematics/college/3ad51tijpkmx4i0lv7shdxwaxv9j3e49ac.png)
Divide both sides by 2:
![x=12](https://img.qammunity.org/2021/formulas/mathematics/middle-school/kzh72we7ptn8hlgavxhsl5e208kjtiramm.png)
Therefore, the value of x is 12.
And we're done!