To find the value of $x$, we need to use the information provided in the diagram.

1. The given angles are $(14x - 25)^\circ$ and $51^\circ$.
2. These two angles form a straight line, meaning they are supplementary. The sum of supplementary angles is $180^\circ$.

So, the equation will be: $(14x - 25) + 51 = 180$

Now, let's solve for $x$.

1. Combine like terms: $14x - 25 + 51 = 180$ $14x + 26 = 180$

2. Subtract 26 from both sides: $14x = 154$

3. Divide both sides by 14: $x = \frac{154}{14} = 11$

Thus, the value of $x$ is $11$.

Would you like further details, or do you have any questions?

Related Questions:

1. How do you identify supplementary angles in a diagram?
2. What is the difference between complementary and supplementary angles?
3. How do you solve equations with multiple variables?
4. What happens if the angles are vertical instead of supplementary?
5. Can you explain how to verify the solution?

Tip:

When solving for unknowns in geometry, always check whether the angles are supplementary, complementary, or vertical to set up the correct equation.