In the provided image, we have a set of intersecting lines and angles. Let's break down the relevant information and the geometric relationship:

• Angles are formed where the lines meet at points such as $E$, $F$, $G$, $D$, and others.
• One angle is given as $73^\circ$, and another angle involves an algebraic expression, $7x - 4^\circ$.

We can use the fact that vertically opposite angles are congruent (equal) when two lines intersect. From the diagram, the angle $7x - 4^\circ$ is vertically opposite to the angle $73^\circ$.

Thus, we can set up the equation: $7x - 4 = 73$

To solve for $x$, follow these steps:

1. Add 4 to both sides of the equation: $7x = 73 + 4$ $7x = 77$

2. Divide both sides by 7: $x = \frac{77}{7}$ $x = 11$

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

Would you like further details or have additional questions?

Here are some related questions for you:

1. How do you identify vertically opposite angles in geometric diagrams?
2. What are the properties of parallel lines and how do they relate to angles?
3. How do you solve for unknown variables in angle equations?
4. What is the relationship between complementary and supplementary angles?
5. Can this method be used in other types of geometric problems involving intersecting lines?

Tip: When solving for angles, always look for relationships such as vertical angles, corresponding angles, or alternate interior angles to set up your equations.