The given triangle has three angles: $50^\circ$, $70^\circ$, and $(6x - 18)^\circ$.

To solve for $x$, we can use the fact that the sum of the interior angles in any triangle is always $180^\circ$.

So, the equation becomes: $50^\circ + 70^\circ + (6x - 18)^\circ = 180^\circ$

Let's solve this step-by-step.

1. Combine the constants on the left-hand side: $120^\circ + (6x - 18)^\circ = 180^\circ$

2. Simplify further: $6x + 102^\circ = 180^\circ$

3. Subtract $102^\circ$ from both sides: $6x = 78^\circ$

4. Divide both sides by 6: $x = 13$

Thus, $x = 13$.

Would you like more details or have any questions?

Related questions:

1. What is the sum of the interior angles of any polygon?
2. How do we verify the solution for $x$ in a triangle?
3. What if one of the angles was unknown? How would we solve it?
4. Can this method be applied to non-Euclidean geometry?
5. What are the properties of an isosceles triangle?

Tip: Always remember that the sum of interior angles in a triangle is always $180^\circ$. This rule is useful in solving for unknown angles!