To solve for $x$ in the given diagram, let's break down the angles.

Key information:

1. The total angle around a point is $360^\circ$.
2. The diagram shows one of the angles marked as $300^\circ$.
3. The other two angles are $x$ and $x + 30^\circ$.

Since the sum of all angles around a point must equal $360^\circ$, we can set up the following equation:

$x + (x + 30^\circ) + 300^\circ = 360^\circ$

Now, let's solve this equation step by step:

1. Combine the terms involving $x$: $2x + 30^\circ + 300^\circ = 360^\circ$

2. Simplify the constants: $2x + 330^\circ = 360^\circ$

3. Subtract $330^\circ$ from both sides: $2x = 30^\circ$

4. Divide both sides by 2: $x = 15^\circ$

Thus, $x = 15^\circ$.

Would you like further details or clarification on any part? Here are some related questions for you:

1. What is the significance of angles around a point summing to $360^\circ$?
2. How would the solution change if the larger angle was not $300^\circ$?
3. Could this same method be used for angles in polygons?
4. How can the concept of supplementary angles help in solving problems like this?
5. How does the calculation change if one of the lines is extended in the opposite direction?

Tip: Always check that all angles around a point add up to $360^\circ$ when solving problems involving rotations.