The diagram you've uploaded shows two intersecting lines, forming angles. The task is to solve for $x$, where one angle is labeled $(8x + 11)^\circ$ and another is given as $73^\circ$. These angles are vertically opposite because they are formed by two intersecting lines, and vertically opposite angles are equal.

We can set up the equation:

$(8x + 11) = 73$

Now, solving for $x$:

$8x + 11 = 73$

Subtract 11 from both sides:

$8x = 62$

Now, divide both sides by 8:

$x = \frac{62}{8} = 7.75$

Thus, $x = 7.75$.

Would you like further details or explanations? Here are five related questions to deepen your understanding:

1. What are the properties of vertically opposite angles?
2. How would the calculation change if the angles were supplementary instead of equal?
3. Can we use this method to solve for $x$ if other angles were given in terms of $x$?
4. How do parallel lines influence angle relationships in geometric problems?
5. What are corresponding and alternate interior angles, and how are they related?

Tip: Remember that vertically opposite angles are always equal when two lines intersect!