To solve for $x$ in the given diagram:

1. Observe that the angle labeled $2x + 10^\circ$ and the $60^\circ$ angle are vertically opposite angles. Vertically opposite angles are always equal.

2. Therefore, we can set up the equation: $2x + 10 = 60$

3. Solve for $x$ by first isolating $2x$: $2x = 60 - 10$ $2x = 50$

4. Now, divide by 2: $x = 25$

Answer:

The value of $x$ is $25^\circ$.

Would you like further details on this solution, or do you have any other questions?

Here are some related questions you might find useful:

1. How do you identify vertically opposite angles in a diagram?
2. What are the properties of vertically opposite angles?
3. Can vertically opposite angles be used in more complex geometry problems?
4. How would this problem change if the angles were not vertically opposite?
5. What if $PQ$ and $RS$ were not straight lines?

Tip: Remember that vertically opposite angles are always equal when two lines intersect. This property can be very useful for solving various angle-related problems.