To solve for $x$ in the given image, we need to analyze the angles around point $O$.

Observations from the Image:

1. There are five rays extending from point $O$, labeled $A$, $B$, $C$, $D$, and $E$.
2. The angles between these rays are labeled as $x$, $2x$, $3x$, and $4x$.

Approach:

The angles around a point add up to $360^\circ$. So, we can set up the following equation:

$x + 2x + 3x + 4x = 360^\circ$

Solve for $x$:

Combine the terms on the left side:

$10x = 360^\circ$

Now, divide both sides by 10:

$x = 36^\circ$

Conclusion:

The value of $x$ is $36^\circ$.

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:

1. How do we determine the sum of angles around a point?
2. What are alternate methods to verify the result of $x$ in this problem?
3. How would this problem change if one of the angles was labeled differently?
4. Can similar principles be applied to angles in polygons? How?
5. What are other real-life applications of angles around a point?

Tip: When dealing with angles around a point, remember they always add up to $360^\circ$.