The problem states that:

• $POQ$ is a straight line.
• $\angle POR = 4x$
• $\angle QOR = 2x$

Since $POQ$ is a straight line, the sum of the angles on a straight line is $180^\circ$. Thus, we have the equation:

$\angle POR + \angle QOR = 180^\circ$

Substitute the given expressions for the angles:

$4x + 2x = 180^\circ$

Simplifying:

$6x = 180^\circ$

Now, solve for $x$:

$x = \frac{180^\circ}{6} = 30^\circ$

So, the value of $x$ is $30^\circ$.

Would you like more details or have any questions?

Here are 5 related questions for deeper understanding:

1. What would the value of $\angle POR$ and $\angle QOR$ be with $x = 30^\circ$?
2. How would the solution change if $\angle POR$ was given as $3x$ instead of $4x$?
3. What is the sum of angles around a point, and how does it differ from the sum of angles on a straight line?
4. Can you think of a scenario where the angles might form a triangle? What rules would apply?
5. How can you apply the linear pair angle concept in different geometric shapes?

Tip: Always remember that the sum of angles on a straight line is $180^\circ$, a useful fact for solving many geometry problems!